---
_id: '13221'
abstract:
- lang: eng
text: The safety-liveness dichotomy is a fundamental concept in formal languages
which plays a key role in verification. Recently, this dichotomy has been lifted
to quantitative properties, which are arbitrary functions from infinite words
to partially-ordered domains. We look into harnessing the dichotomy for the specific
classes of quantitative properties expressed by quantitative automata. These automata
contain finitely many states and rational-valued transition weights, and their
common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum
map infinite words into the totallyordered domain of real numbers. In this automata-theoretic
setting, we establish a connection between quantitative safety and topological
continuity and provide an alternative characterization of quantitative safety
and liveness in terms of their boolean counterparts. For all common value functions,
we show how the safety closure of a quantitative automaton can be constructed
in PTime, and we provide PSpace-complete checks of whether a given quantitative
automaton is safe or live, with the exception of LimInfAvg and LimSupAvg automata,
for which the safety check is in ExpSpace. Moreover, for deterministic Sup, LimInf,
and LimSup automata, we give PTime decompositions into safe and live automata.
These decompositions enable the separation of techniques for safety and liveness
verification for quantitative specifications.
acknowledgement: We thank Christof Löding for pointing us to some results on PSpace-hardess
of universality problems and the anonymous reviewers for their helpful comments.
This work was supported in part by the ERC-2020-AdG 101020093 and the Israel Science
Foundation grant 2410/22.
alternative_title:
- LIPIcs
article_number: '17'
article_processing_charge: No
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000-0002-2985-7724
- first_name: Nicolas Adrien
full_name: Mazzocchi, Nicolas Adrien
id: b26baa86-3308-11ec-87b0-8990f34baa85
last_name: Mazzocchi
- first_name: Naci E
full_name: Sarac, Naci E
id: 8C6B42F8-C8E6-11E9-A03A-F2DCE5697425
last_name: Sarac
citation:
ama: 'Boker U, Henzinger TA, Mazzocchi NA, Sarac NE. Safety and liveness of quantitative
automata. In: 34th International Conference on Concurrency Theory. Vol
279. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.CONCUR.2023.17'
apa: 'Boker, U., Henzinger, T. A., Mazzocchi, N. A., & Sarac, N. E. (2023).
Safety and liveness of quantitative automata. In 34th International Conference
on Concurrency Theory (Vol. 279). Antwerp, Belgium: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.CONCUR.2023.17'
chicago: Boker, Udi, Thomas A Henzinger, Nicolas Adrien Mazzocchi, and Naci E Sarac.
“Safety and Liveness of Quantitative Automata.” In 34th International Conference
on Concurrency Theory, Vol. 279. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023. https://doi.org/10.4230/LIPIcs.CONCUR.2023.17.
ieee: U. Boker, T. A. Henzinger, N. A. Mazzocchi, and N. E. Sarac, “Safety and liveness
of quantitative automata,” in 34th International Conference on Concurrency
Theory, Antwerp, Belgium, 2023, vol. 279.
ista: 'Boker U, Henzinger TA, Mazzocchi NA, Sarac NE. 2023. Safety and liveness
of quantitative automata. 34th International Conference on Concurrency Theory.
CONCUR: Conference on Concurrency Theory, LIPIcs, vol. 279, 17.'
mla: Boker, Udi, et al. “Safety and Liveness of Quantitative Automata.” 34th
International Conference on Concurrency Theory, vol. 279, 17, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPIcs.CONCUR.2023.17.
short: U. Boker, T.A. Henzinger, N.A. Mazzocchi, N.E. Sarac, in:, 34th International
Conference on Concurrency Theory, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023.
conference:
end_date: 2023-09-23
location: Antwerp, Belgium
name: 'CONCUR: Conference on Concurrency Theory'
start_date: 2023-09-18
date_created: 2023-07-14T10:00:15Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2023-10-09T07:14:03Z
day: '01'
ddc:
- '000'
department:
- _id: GradSch
- _id: ToHe
doi: 10.4230/LIPIcs.CONCUR.2023.17
ec_funded: 1
external_id:
arxiv:
- '2307.06016'
file:
- access_level: open_access
checksum: d40e57a04448ea5c77d7e1cfb9590a81
content_type: application/pdf
creator: esarac
date_created: 2023-07-14T12:03:48Z
date_updated: 2023-07-14T12:03:48Z
file_id: '13224'
file_name: CONCUR23.pdf
file_size: 755529
relation: main_file
success: 1
file_date_updated: 2023-07-14T12:03:48Z
has_accepted_license: '1'
intvolume: ' 279'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 62781420-2b32-11ec-9570-8d9b63373d4d
call_identifier: H2020
grant_number: '101020093'
name: Vigilant Algorithmic Monitoring of Software
publication: 34th International Conference on Concurrency Theory
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959772990'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
status: public
title: Safety and liveness of quantitative automata
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 279
year: '2023'
...
---
_id: '1659'
abstract:
- lang: eng
text: 'The target discounted-sum problem is the following: Given a rational discount
factor 0 < λ < 1 and three rational values a, b, and t, does there exist
a finite or an infinite sequence w ε(a, b)∗ or w ε(a, b)w, such that Σ|w| i=0
w(i)λi equals t? The problem turns out to relate to many fields of mathematics
and computer science, and its decidability question is surprisingly hard to solve.
We solve the finite version of the problem, and show the hardness of the infinite
version, linking it to various areas and open problems in mathematics and computer
science: β-expansions, discounted-sum automata, piecewise affine maps, and generalizations
of the Cantor set. We provide some partial results to the infinite version, among
which are solutions to its restriction to eventually-periodic sequences and to
the cases that λ λ 1/2 or λ = 1/n, for every n ε N. We use our results for solving
some open problems on discounted-sum automata, among which are the exact-value
problem for nondeterministic automata over finite words and the universality and
inclusion problems for functional automata.'
acknowledgement: 'A technical report of the article is available at: https://research-explorer.app.ist.ac.at/record/5439'
article_processing_charge: No
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Jan
full_name: Otop, Jan
id: 2FC5DA74-F248-11E8-B48F-1D18A9856A87
last_name: Otop
citation:
ama: 'Boker U, Henzinger TA, Otop J. The target discounted-sum problem. In: LICS.
Logic in Computer Science. IEEE; 2015:750-761. doi:10.1109/LICS.2015.74'
apa: 'Boker, U., Henzinger, T. A., & Otop, J. (2015). The target discounted-sum
problem. In LICS (pp. 750–761). Kyoto, Japan: IEEE. https://doi.org/10.1109/LICS.2015.74'
chicago: Boker, Udi, Thomas A Henzinger, and Jan Otop. “The Target Discounted-Sum
Problem.” In LICS, 750–61. Logic in Computer Science. IEEE, 2015. https://doi.org/10.1109/LICS.2015.74.
ieee: U. Boker, T. A. Henzinger, and J. Otop, “The target discounted-sum problem,”
in LICS, Kyoto, Japan, 2015, pp. 750–761.
ista: 'Boker U, Henzinger TA, Otop J. 2015. The target discounted-sum problem. LICS.
LICS: Logic in Computer ScienceLogic in Computer Science, 750–761.'
mla: Boker, Udi, et al. “The Target Discounted-Sum Problem.” LICS, IEEE,
2015, pp. 750–61, doi:10.1109/LICS.2015.74.
short: U. Boker, T.A. Henzinger, J. Otop, in:, LICS, IEEE, 2015, pp. 750–761.
conference:
end_date: 2015-07-10
location: Kyoto, Japan
name: 'LICS: Logic in Computer Science'
start_date: 2015-007-06
date_created: 2018-12-11T11:53:19Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2023-02-23T12:26:27Z
day: '01'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1109/LICS.2015.74
ec_funded: 1
file:
- access_level: open_access
checksum: 6abebca9c1a620e9e103a8f9222befac
content_type: application/pdf
creator: dernst
date_created: 2020-05-15T08:53:29Z
date_updated: 2020-07-14T12:45:10Z
file_id: '7852'
file_name: 2015_LICS_Boker.pdf
file_size: 340215
relation: main_file
file_date_updated: 2020-07-14T12:45:10Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Submitted Version
page: 750 - 761
project:
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication: LICS
publication_identifier:
eisbn:
- '978-1-4799-8875-4 '
issn:
- '1043-6871 '
publication_status: published
publisher: IEEE
publist_id: '5491'
quality_controlled: '1'
related_material:
record:
- id: '5439'
relation: earlier_version
status: public
scopus_import: 1
series_title: Logic in Computer Science
status: public
title: The target discounted-sum problem
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '5439'
abstract:
- lang: eng
text: 'The target discounted-sum problem is the following: Given a rational discount
factor 0 < λ < 1 and three rational values a, b, and t, does there exist a finite
or an infinite sequence w ε(a, b)∗ or w ε(a, b)w, such that Σ|w| i=0 w(i)λi equals
t? The problem turns out to relate to many fields of mathematics and computer
science, and its decidability question is surprisingly hard to solve. We solve
the finite version of the problem, and show the hardness of the infinite version,
linking it to various areas and open problems in mathematics and computer science:
β-expansions, discounted-sum automata, piecewise affine maps, and generalizations
of the Cantor set. We provide some partial results to the infinite version, among
which are solutions to its restriction to eventually-periodic sequences and to
the cases that λ λ 1/2 or λ = 1/n, for every n ε N. We use our results for solving
some open problems on discounted-sum automata, among which are the exact-value
problem for nondeterministic automata over finite words and the universality and
inclusion problems for functional automata. '
alternative_title:
- IST Austria Technical Report
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Jan
full_name: Otop, Jan
id: 2FC5DA74-F248-11E8-B48F-1D18A9856A87
last_name: Otop
citation:
ama: Boker U, Henzinger TA, Otop J. The Target Discounted-Sum Problem. IST
Austria; 2015. doi:10.15479/AT:IST-2015-335-v1-1
apa: Boker, U., Henzinger, T. A., & Otop, J. (2015). The target discounted-sum
problem. IST Austria. https://doi.org/10.15479/AT:IST-2015-335-v1-1
chicago: Boker, Udi, Thomas A Henzinger, and Jan Otop. The Target Discounted-Sum
Problem. IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-335-v1-1.
ieee: U. Boker, T. A. Henzinger, and J. Otop, The target discounted-sum problem.
IST Austria, 2015.
ista: Boker U, Henzinger TA, Otop J. 2015. The target discounted-sum problem, IST
Austria, 20p.
mla: Boker, Udi, et al. The Target Discounted-Sum Problem. IST Austria, 2015,
doi:10.15479/AT:IST-2015-335-v1-1.
short: U. Boker, T.A. Henzinger, J. Otop, The Target Discounted-Sum Problem, IST
Austria, 2015.
date_created: 2018-12-12T11:39:20Z
date_published: 2015-05-18T00:00:00Z
date_updated: 2023-02-23T10:08:48Z
day: '18'
ddc:
- '004'
- '512'
- '513'
department:
- _id: ToHe
doi: 10.15479/AT:IST-2015-335-v1-1
file:
- access_level: open_access
checksum: 40405907aa012acece1bc26cf0be554d
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:53:55Z
date_updated: 2020-07-14T12:46:55Z
file_id: '5517'
file_name: IST-2015-335-v1+1_report.pdf
file_size: 589619
relation: main_file
file_date_updated: 2020-07-14T12:46:55Z
has_accepted_license: '1'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: '20'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '335'
related_material:
record:
- id: '1659'
relation: later_version
status: public
status: public
title: The target discounted-sum problem
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '2239'
abstract:
- lang: eng
text: The analysis of the energy consumption of software is an important goal for
quantitative formal methods. Current methods, using weighted transition systems
or energy games, model the energy source as an ideal resource whose status is
characterized by one number, namely the amount of remaining energy. Real batteries,
however, exhibit behaviors that can deviate substantially from an ideal energy
resource. Based on a discretization of a standard continuous battery model, we
introduce battery transition systems. In this model, a battery is viewed as consisting
of two parts-the available-charge tank and the bound-charge tank. Any charge or
discharge is applied to the available-charge tank. Over time, the energy from
each tank diffuses to the other tank. Battery transition systems are infinite
state systems that, being not well-structured, fall into no decidable class that
is known to us. Nonetheless, we are able to prove that the !-regular modelchecking
problem is decidable for battery transition systems. We also present a case study
on the verification of control programs for energy-constrained semi-autonomous
robots.
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Arjun
full_name: Radhakrishna, Arjun
id: 3B51CAC4-F248-11E8-B48F-1D18A9856A87
last_name: Radhakrishna
citation:
ama: 'Boker U, Henzinger TA, Radhakrishna A. Battery transition systems. In: Vol
49. ACM; 2014:595-606. doi:10.1145/2535838.2535875'
apa: 'Boker, U., Henzinger, T. A., & Radhakrishna, A. (2014). Battery transition
systems (Vol. 49, pp. 595–606). Presented at the POPL: Principles of Programming
Languages, San Diego, USA: ACM. https://doi.org/10.1145/2535838.2535875'
chicago: Boker, Udi, Thomas A Henzinger, and Arjun Radhakrishna. “Battery Transition
Systems,” 49:595–606. ACM, 2014. https://doi.org/10.1145/2535838.2535875.
ieee: 'U. Boker, T. A. Henzinger, and A. Radhakrishna, “Battery transition systems,”
presented at the POPL: Principles of Programming Languages, San Diego, USA, 2014,
vol. 49, no. 1, pp. 595–606.'
ista: 'Boker U, Henzinger TA, Radhakrishna A. 2014. Battery transition systems.
POPL: Principles of Programming Languages vol. 49, 595–606.'
mla: Boker, Udi, et al. Battery Transition Systems. Vol. 49, no. 1, ACM,
2014, pp. 595–606, doi:10.1145/2535838.2535875.
short: U. Boker, T.A. Henzinger, A. Radhakrishna, in:, ACM, 2014, pp. 595–606.
conference:
end_date: 2014-01-24
location: San Diego, USA
name: 'POPL: Principles of Programming Languages'
start_date: 2014-01-22
date_created: 2018-12-11T11:56:30Z
date_published: 2014-01-13T00:00:00Z
date_updated: 2021-01-12T06:56:13Z
day: '13'
department:
- _id: ToHe
doi: 10.1145/2535838.2535875
ec_funded: 1
intvolume: ' 49'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 595 - 606
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
publication_identifier:
isbn:
- 978-145032544-8
publication_status: published
publisher: ACM
publist_id: '4722'
quality_controlled: '1'
scopus_import: 1
status: public
title: Battery transition systems
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 49
year: '2014'
...
---
_id: '2038'
abstract:
- lang: eng
text: Recently, there has been an effort to add quantitative objectives to formal
verification and synthesis. We introduce and investigate the extension of temporal
logics with quantitative atomic assertions. At the heart of quantitative objectives
lies the accumulation of values along a computation. It is often the accumulated
sum, as with energy objectives, or the accumulated average, as with mean-payoff
objectives. We investigate the extension of temporal logics with the prefix-accumulation
assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric (or Boolean) variable
of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the
accumulated sum and average of the values of v from the beginning of the computation
up to the current point in time. We also allow the path-accumulation assertions
LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an
entire infinite computation. We study the border of decidability for such quantitative
extensions of various temporal logics. In particular, we show that extending the
fragment of CTL that has only the EX, EF, AX, and AG temporal modalities with
both prefix-accumulation assertions, or extending LTL with both path-accumulation
assertions, results in temporal logics whose model-checking problem is decidable.
Moreover, the prefix-accumulation assertions may be generalized with "controlled
accumulation," allowing, for example, to specify constraints on the average
waiting time between a request and a grant. On the negative side, we show that
this branching-time logic is, in a sense, the maximal logic with one or both of
the prefix-accumulation assertions that permits a decidable model-checking procedure.
Extending a temporal logic that has the EG or EU modalities, such as CTL or LTL,
makes the problem undecidable.
acknowledgement: The research was supported in part by ERC Starting grant 278410 (QUALITY).
article_number: '27'
article_processing_charge: No
article_type: original
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Orna
full_name: Kupferman, Orna
last_name: Kupferman
citation:
ama: Boker U, Chatterjee K, Henzinger TA, Kupferman O. Temporal specifications with
accumulative values. ACM Transactions on Computational Logic (TOCL). 2014;15(4).
doi:10.1145/2629686
apa: Boker, U., Chatterjee, K., Henzinger, T. A., & Kupferman, O. (2014). Temporal
specifications with accumulative values. ACM Transactions on Computational
Logic (TOCL). ACM. https://doi.org/10.1145/2629686
chicago: Boker, Udi, Krishnendu Chatterjee, Thomas A Henzinger, and Orna Kupferman.
“Temporal Specifications with Accumulative Values.” ACM Transactions on Computational
Logic (TOCL). ACM, 2014. https://doi.org/10.1145/2629686.
ieee: U. Boker, K. Chatterjee, T. A. Henzinger, and O. Kupferman, “Temporal specifications
with accumulative values,” ACM Transactions on Computational Logic (TOCL),
vol. 15, no. 4. ACM, 2014.
ista: Boker U, Chatterjee K, Henzinger TA, Kupferman O. 2014. Temporal specifications
with accumulative values. ACM Transactions on Computational Logic (TOCL). 15(4),
27.
mla: Boker, Udi, et al. “Temporal Specifications with Accumulative Values.” ACM
Transactions on Computational Logic (TOCL), vol. 15, no. 4, 27, ACM, 2014,
doi:10.1145/2629686.
short: U. Boker, K. Chatterjee, T.A. Henzinger, O. Kupferman, ACM Transactions on
Computational Logic (TOCL) 15 (2014).
date_created: 2018-12-11T11:55:21Z
date_published: 2014-09-16T00:00:00Z
date_updated: 2023-02-23T12:23:54Z
day: '16'
ddc:
- '000'
- '004'
department:
- _id: ToHe
- _id: KrCh
doi: 10.1145/2629686
ec_funded: 1
file:
- access_level: open_access
checksum: 354c41d37500b56320afce94cf9a99c2
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:59Z
date_updated: 2020-07-14T12:45:26Z
file_id: '4851'
file_name: IST-2014-192-v1+1_AccumulativeValues.pdf
file_size: 346184
relation: main_file
file_date_updated: 2020-07-14T12:45:26Z
has_accepted_license: '1'
intvolume: ' 15'
issue: '4'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Submitted Version
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25F5A88A-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11402-N23
name: Moderne Concurrency Paradigms
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication: ACM Transactions on Computational Logic (TOCL)
publication_status: published
publisher: ACM
publist_id: '5013'
pubrep_id: '192'
quality_controlled: '1'
related_material:
record:
- id: '3356'
relation: earlier_version
status: public
- id: '5385'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Temporal specifications with accumulative values
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2014'
...
---
_id: '1387'
abstract:
- lang: eng
text: Choices made by nondeterministic word automata depend on both the past (the
prefix of the word read so far) and the future (the suffix yet to be read). In
several applications, most notably synthesis, the future is diverse or unknown,
leading to algorithms that are based on deterministic automata. Hoping to retain
some of the advantages of nondeterministic automata, researchers have studied
restricted classes of nondeterministic automata. Three such classes are nondeterministic
automata that are good for trees (GFT; i.e., ones that can be expanded to tree
automata accepting the derived tree languages, thus whose choices should satisfy
diverse futures), good for games (GFG; i.e., ones whose choices depend only on
the past), and determinizable by pruning (DBP; i.e., ones that embody equivalent
deterministic automata). The theoretical properties and relative merits of the
different classes are still open, having vagueness on whether they really differ
from deterministic automata. In particular, while DBP ⊆ GFG ⊆ GFT, it is not known
whether every GFT automaton is GFG and whether every GFG automaton is DBP. Also
open is the possible succinctness of GFG and GFT automata compared to deterministic
automata. We study these problems for ω-regular automata with all common acceptance
conditions. We show that GFT=GFG⊃DBP, and describe a determinization construction
for GFG automata.
acknowledgement: and ERC Grant QUALITY.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Denis
full_name: Kuperberg, Denis
last_name: Kuperberg
- first_name: Orna
full_name: Kupferman, Orna
last_name: Kupferman
- first_name: Michał
full_name: Skrzypczak, Michał
last_name: Skrzypczak
citation:
ama: Boker U, Kuperberg D, Kupferman O, Skrzypczak M. Nondeterminism in the presence
of a diverse or unknown future. 2013;7966(PART 2):89-100. doi:10.1007/978-3-642-39212-2_11
apa: 'Boker, U., Kuperberg, D., Kupferman, O., & Skrzypczak, M. (2013). Nondeterminism
in the presence of a diverse or unknown future. Presented at the ICALP: Automata,
Languages and Programming, Riga, Latvia: Springer. https://doi.org/10.1007/978-3-642-39212-2_11'
chicago: Boker, Udi, Denis Kuperberg, Orna Kupferman, and Michał Skrzypczak. “Nondeterminism
in the Presence of a Diverse or Unknown Future.” Lecture Notes in Computer Science.
Springer, 2013. https://doi.org/10.1007/978-3-642-39212-2_11.
ieee: U. Boker, D. Kuperberg, O. Kupferman, and M. Skrzypczak, “Nondeterminism in
the presence of a diverse or unknown future,” vol. 7966, no. PART 2. Springer,
pp. 89–100, 2013.
ista: Boker U, Kuperberg D, Kupferman O, Skrzypczak M. 2013. Nondeterminism in the
presence of a diverse or unknown future. 7966(PART 2), 89–100.
mla: Boker, Udi, et al. Nondeterminism in the Presence of a Diverse or Unknown
Future. Vol. 7966, no. PART 2, Springer, 2013, pp. 89–100, doi:10.1007/978-3-642-39212-2_11.
short: U. Boker, D. Kuperberg, O. Kupferman, M. Skrzypczak, 7966 (2013) 89–100.
conference:
end_date: 2013-07-12
location: Riga, Latvia
name: 'ICALP: Automata, Languages and Programming'
start_date: 2013-07-08
date_created: 2018-12-11T11:51:44Z
date_published: 2013-07-01T00:00:00Z
date_updated: 2020-08-11T10:09:09Z
day: '01'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/978-3-642-39212-2_11
ec_funded: 1
file:
- access_level: open_access
checksum: 98bc02e3793072e279ec8d364b381ff3
content_type: application/pdf
creator: dernst
date_created: 2020-05-15T11:05:50Z
date_updated: 2020-07-14T12:44:48Z
file_id: '7857'
file_name: 2013_ICALP_Boker.pdf
file_size: 276982
relation: main_file
file_date_updated: 2020-07-14T12:44:48Z
has_accepted_license: '1'
intvolume: ' 7966'
issue: PART 2
language:
- iso: eng
month: '07'
oa: 1
oa_version: Submitted Version
page: 89 - 100
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
publication_status: published
publisher: Springer
publist_id: '5823'
quality_controlled: '1'
scopus_import: 1
series_title: Lecture Notes in Computer Science
status: public
title: Nondeterminism in the presence of a diverse or unknown future
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7966
year: '2013'
...
---
_id: '2517'
abstract:
- lang: eng
text: 'Traditional formal methods are based on a Boolean satisfaction notion: a
reactive system satisfies, or not, a given specification. We generalize formal
methods to also address the quality of systems. As an adequate specification formalism
we introduce the linear temporal logic LTL[F]. The satisfaction value of an LTL[F]
formula is a number between 0 and 1, describing the quality of the satisfaction.
The logic generalizes traditional LTL by augmenting it with a (parameterized)
set F of arbitrary functions over the interval [0,1]. For example, F may contain
the maximum or minimum between the satisfaction values of subformulas, their product,
and their average. The classical decision problems in formal methods, such as
satisfiability, model checking, and synthesis, are generalized to search and optimization
problems in the quantitative setting. For example, model checking asks for the
quality in which a specification is satisfied, and synthesis returns a system
satisfying the specification with the highest quality. Reasoning about quality
gives rise to other natural questions, like the distance between specifications.
We formalize these basic questions and study them for LTL[F]. By extending the
automata-theoretic approach for LTL to a setting that takes quality into an account,
we are able to solve the above problems and show that reasoning about LTL[F] has
roughly the same complexity as reasoning about traditional LTL.'
acknowledgement: 'ERC Grant QUALITY. '
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Shaull
full_name: Almagor, Shaull
last_name: Almagor
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Orna
full_name: Kupferman, Orna
last_name: Kupferman
citation:
ama: Almagor S, Boker U, Kupferman O. Formalizing and reasoning about quality. 2013;7966(Part
2):15-27. doi:10.1007/978-3-642-39212-2_3
apa: 'Almagor, S., Boker, U., & Kupferman, O. (2013). Formalizing and reasoning
about quality. Presented at the ICALP: Automata, Languages and Programming, Riga,
Latvia: Springer. https://doi.org/10.1007/978-3-642-39212-2_3'
chicago: Almagor, Shaull, Udi Boker, and Orna Kupferman. “Formalizing and Reasoning
about Quality.” Lecture Notes in Computer Science. Springer, 2013. https://doi.org/10.1007/978-3-642-39212-2_3.
ieee: S. Almagor, U. Boker, and O. Kupferman, “Formalizing and reasoning about quality,”
vol. 7966, no. Part 2. Springer, pp. 15–27, 2013.
ista: Almagor S, Boker U, Kupferman O. 2013. Formalizing and reasoning about quality.
7966(Part 2), 15–27.
mla: Almagor, Shaull, et al. Formalizing and Reasoning about Quality. Vol.
7966, no. Part 2, Springer, 2013, pp. 15–27, doi:10.1007/978-3-642-39212-2_3.
short: S. Almagor, U. Boker, O. Kupferman, 7966 (2013) 15–27.
conference:
end_date: 2013-07-12
location: Riga, Latvia
name: 'ICALP: Automata, Languages and Programming'
start_date: 2013-07-08
date_created: 2018-12-11T11:58:08Z
date_published: 2013-07-01T00:00:00Z
date_updated: 2020-08-11T10:09:47Z
day: '01'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/978-3-642-39212-2_3
ec_funded: 1
file:
- access_level: open_access
checksum: 85afbf6c18a2c7e377c52c9410e2d824
content_type: application/pdf
creator: dernst
date_created: 2020-05-15T11:16:12Z
date_updated: 2020-07-14T12:45:42Z
file_id: '7860'
file_name: 2013_ICALP_Almagor.pdf
file_size: 363031
relation: main_file
file_date_updated: 2020-07-14T12:45:42Z
has_accepted_license: '1'
intvolume: ' 7966'
issue: Part 2
language:
- iso: eng
month: '07'
oa: 1
oa_version: Submitted Version
page: 15 - 27
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
publication_status: published
publisher: Springer
publist_id: '4384'
quality_controlled: '1'
scopus_import: 1
series_title: Lecture Notes in Computer Science
status: public
title: Formalizing and reasoning about quality
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7966
year: '2013'
...
---
_id: '2891'
abstract:
- lang: eng
text: "Quantitative automata are nondeterministic finite automata with edge weights.
They value a\r\nrun by some function from the sequence of visited weights to the
reals, and value a word by its\r\nminimal/maximal run. They generalize boolean
automata, and have gained much attention in\r\nrecent years. Unfortunately, important
automaton classes, such as sum, discounted-sum, and\r\nlimit-average automata,
cannot be determinized. Yet, the quantitative setting provides the potential\r\nof
approximate determinization. We define approximate determinization with respect
to\r\na distance function, and investigate this potential.\r\nWe show that sum
automata cannot be determinized approximately with respect to any\r\ndistance
function. However, restricting to nonnegative weights allows for approximate determinization\r\nwith
respect to some distance functions.\r\nDiscounted-sum automata allow for approximate
determinization, as the influence of a word’s\r\nsuffix is decaying. However,
the naive approach, of unfolding the automaton computations up\r\nto a sufficient
level, is shown to be doubly exponential in the discount factor. We provide an\r\nalternative
construction that is singly exponential in the discount factor, in the precision,
and\r\nin the number of states. We prove matching lower bounds, showing exponential
dependency on\r\neach of these three parameters.\r\nAverage and limit-average
automata are shown to prohibit approximate determinization with\r\nrespect to
any distance function, and this is the case even for two weights, 0 and 1."
acknowledgement: We thank Laurent Doyen for great ideas and valuable help in analyzing
discounted-sum automata.
alternative_title:
- LIPIcs
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
citation:
ama: 'Boker U, Henzinger TA. Approximate determinization of quantitative automata.
In: Leibniz International Proceedings in Informatics. Vol 18. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik; 2012:362-373. doi:10.4230/LIPIcs.FSTTCS.2012.362'
apa: 'Boker, U., & Henzinger, T. A. (2012). Approximate determinization of quantitative
automata. In Leibniz International Proceedings in Informatics (Vol. 18,
pp. 362–373). Hyderabad, India: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.FSTTCS.2012.362'
chicago: Boker, Udi, and Thomas A Henzinger. “Approximate Determinization of Quantitative
Automata.” In Leibniz International Proceedings in Informatics, 18:362–73.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012. https://doi.org/10.4230/LIPIcs.FSTTCS.2012.362.
ieee: U. Boker and T. A. Henzinger, “Approximate determinization of quantitative
automata,” in Leibniz International Proceedings in Informatics, Hyderabad,
India, 2012, vol. 18, pp. 362–373.
ista: 'Boker U, Henzinger TA. 2012. Approximate determinization of quantitative
automata. Leibniz International Proceedings in Informatics. FSTTCS: Foundations
of Software Technology and Theoretical Computer Science, LIPIcs, vol. 18, 362–373.'
mla: Boker, Udi, and Thomas A. Henzinger. “Approximate Determinization of Quantitative
Automata.” Leibniz International Proceedings in Informatics, vol. 18, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2012, pp. 362–73, doi:10.4230/LIPIcs.FSTTCS.2012.362.
short: U. Boker, T.A. Henzinger, in:, Leibniz International Proceedings in Informatics,
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012, pp. 362–373.
conference:
end_date: 2012-12-17
location: Hyderabad, India
name: 'FSTTCS: Foundations of Software Technology and Theoretical Computer Science'
start_date: 2012-12-15
date_created: 2018-12-11T12:00:10Z
date_published: 2012-12-01T00:00:00Z
date_updated: 2021-01-12T07:00:31Z
day: '01'
ddc:
- '004'
department:
- _id: ToHe
doi: 10.4230/LIPIcs.FSTTCS.2012.362
ec_funded: 1
file:
- access_level: open_access
checksum: 88da18d3e2cb2e5011d7d10ce38a3864
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:37Z
date_updated: 2020-07-14T12:45:52Z
file_id: '4826'
file_name: IST-2017-805-v1+1_34.pdf
file_size: 559069
relation: main_file
file_date_updated: 2020-07-14T12:45:52Z
has_accepted_license: '1'
intvolume: ' 18'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '12'
oa: 1
oa_version: Published Version
page: 362 - 373
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
publication: Leibniz International Proceedings in Informatics
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '3867'
pubrep_id: '805'
quality_controlled: '1'
scopus_import: 1
status: public
title: Approximate determinization of quantitative automata
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 18
year: '2012'
...
---
_id: '494'
abstract:
- lang: eng
text: We solve the longstanding open problems of the blow-up involved in the translations,
when possible, of a nondeterministic Büchi word automaton (NBW) to a nondeterministic
co-Büchi word automaton (NCW) and to a deterministic co-Büchi word automaton (DCW).
For the NBW to NCW translation, the currently known upper bound is 2o(nlog n)
and the lower bound is 1.5n. We improve the upper bound to n2n and describe a
matching lower bound of 2ω(n). For the NBW to DCW translation, the currently known
upper bound is 2o(nlog n). We improve it to 2 o(n), which is asymptotically tight.
Both of our upper-bound constructions are based on a simple subset construction,
do not involve intermediate automata with richer acceptance conditions, and can
be implemented symbolically. We continue and solve the open problems of translating
nondeterministic Streett, Rabin, Muller, and parity word automata to NCW and to
DCW. Going via an intermediate NBW is not optimal and we describe direct, simple,
and asymptotically tight constructions, involving a 2o(n) blow-up. The constructions
are variants of the subset construction, providing a unified approach for translating
all common classes of automata to NCW and DCW. Beyond the theoretical importance
of the results, we point to numerous applications of the new constructions. In
particular, they imply a simple subset-construction based translation, when possible,
of LTL to deterministic Büchi word automata.
article_number: '29'
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Orna
full_name: Kupferman, Orna
last_name: Kupferman
citation:
ama: Boker U, Kupferman O. Translating to Co-Büchi made tight, unified, and useful.
ACM Transactions on Computational Logic (TOCL). 2012;13(4). doi:10.1145/2362355.2362357
apa: Boker, U., & Kupferman, O. (2012). Translating to Co-Büchi made tight,
unified, and useful. ACM Transactions on Computational Logic (TOCL). ACM.
https://doi.org/10.1145/2362355.2362357
chicago: Boker, Udi, and Orna Kupferman. “Translating to Co-Büchi Made Tight, Unified,
and Useful.” ACM Transactions on Computational Logic (TOCL). ACM, 2012.
https://doi.org/10.1145/2362355.2362357.
ieee: U. Boker and O. Kupferman, “Translating to Co-Büchi made tight, unified, and
useful,” ACM Transactions on Computational Logic (TOCL), vol. 13, no. 4.
ACM, 2012.
ista: Boker U, Kupferman O. 2012. Translating to Co-Büchi made tight, unified, and
useful. ACM Transactions on Computational Logic (TOCL). 13(4), 29.
mla: Boker, Udi, and Orna Kupferman. “Translating to Co-Büchi Made Tight, Unified,
and Useful.” ACM Transactions on Computational Logic (TOCL), vol. 13, no.
4, 29, ACM, 2012, doi:10.1145/2362355.2362357.
short: U. Boker, O. Kupferman, ACM Transactions on Computational Logic (TOCL) 13
(2012).
date_created: 2018-12-11T11:46:47Z
date_published: 2012-10-01T00:00:00Z
date_updated: 2021-01-12T08:01:03Z
day: '01'
department:
- _id: ToHe
doi: 10.1145/2362355.2362357
intvolume: ' 13'
issue: '4'
language:
- iso: eng
month: '10'
oa_version: None
publication: ACM Transactions on Computational Logic (TOCL)
publication_status: published
publisher: ACM
publist_id: '7326'
quality_controlled: '1'
scopus_import: 1
status: public
title: Translating to Co-Büchi made tight, unified, and useful
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 13
year: '2012'
...
---
_id: '3326'
abstract:
- lang: eng
text: 'Weighted automata map input words to numerical values. Ap- plications of
weighted automata include formal verification of quantitative properties, as well
as text, speech, and image processing. A weighted au- tomaton is defined with
respect to a semiring. For the tropical semiring, the weight of a run is the sum
of the weights of the transitions taken along the run, and the value of a word
is the minimal weight of an accepting run on it. In the 90’s, Krob studied the
decidability of problems on rational series defined with respect to the tropical
semiring. Rational series are strongly related to weighted automata, and Krob’s
results apply to them. In par- ticular, it follows from Krob’s results that the
universality problem (that is, deciding whether the values of all words are below
some threshold) is decidable for weighted automata defined with respect to the
tropical semir- ing with domain ∪ {∞}, and that the equality problem is undecidable
when the domain is ∪ {∞}. In this paper we continue the study of the borders of
decidability in weighted automata, describe alternative and direct proofs of the
above results, and tighten them further. Unlike the proofs of Krob, which are
algebraic in their nature, our proofs stay in the terrain of state machines, and
the reduction is from the halting problem of a two-counter machine. This enables
us to significantly simplify Krob’s reasoning, make the un- decidability result
accessible to the automata-theoretic community, and strengthen it to apply already
to a very simple class of automata: all the states are accepting, there are no
initial nor final weights, and all the weights on the transitions are from the
set {−1, 0, 1}. The fact we work directly with the automata enables us to tighten
also the decidability re- sults and to show that the universality problem for
weighted automata defined with respect to the tropical semiring with domain ∪
{∞}, and in fact even with domain ≥0 ∪ {∞}, is PSPACE-complete. Our results thus
draw a sharper picture about the decidability of decision problems for weighted
automata, in both the front of containment vs. universality and the front of the
∪ {∞} vs. the ∪ {∞} domains.'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Shaull
full_name: Almagor, Shaull
last_name: Almagor
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Orna
full_name: Kupferman, Orna
last_name: Kupferman
citation:
ama: 'Almagor S, Boker U, Kupferman O. What’s decidable about weighted automata
. In: Vol 6996. Springer; 2011:482-491. doi:10.1007/978-3-642-24372-1_37'
apa: 'Almagor, S., Boker, U., & Kupferman, O. (2011). What’s decidable about
weighted automata (Vol. 6996, pp. 482–491). Presented at the ATVA: Automated
Technology for Verification and Analysis, Taipei, Taiwan: Springer. https://doi.org/10.1007/978-3-642-24372-1_37'
chicago: Almagor, Shaull, Udi Boker, and Orna Kupferman. “What’s Decidable about
Weighted Automata ,” 6996:482–91. Springer, 2011. https://doi.org/10.1007/978-3-642-24372-1_37.
ieee: 'S. Almagor, U. Boker, and O. Kupferman, “What’s decidable about weighted
automata ,” presented at the ATVA: Automated Technology for Verification and Analysis,
Taipei, Taiwan, 2011, vol. 6996, pp. 482–491.'
ista: 'Almagor S, Boker U, Kupferman O. 2011. What’s decidable about weighted automata
. ATVA: Automated Technology for Verification and Analysis, LNCS, vol. 6996, 482–491.'
mla: Almagor, Shaull, et al. What’s Decidable about Weighted Automata . Vol.
6996, Springer, 2011, pp. 482–91, doi:10.1007/978-3-642-24372-1_37.
short: S. Almagor, U. Boker, O. Kupferman, in:, Springer, 2011, pp. 482–491.
conference:
end_date: 2011-10-14
location: Taipei, Taiwan
name: 'ATVA: Automated Technology for Verification and Analysis'
start_date: 2011-10-11
date_created: 2018-12-11T12:02:41Z
date_published: 2011-10-14T00:00:00Z
date_updated: 2021-01-12T07:42:40Z
day: '14'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/978-3-642-24372-1_37
file:
- access_level: open_access
checksum: a7ca08a2cb1b6925f4c18a3034ae5659
content_type: application/pdf
creator: dernst
date_created: 2020-05-19T16:08:32Z
date_updated: 2020-07-14T12:46:07Z
file_id: '7868'
file_name: 2011_LNCS_Almagor.pdf
file_size: 182309
relation: main_file
file_date_updated: 2020-07-14T12:46:07Z
has_accepted_license: '1'
intvolume: ' 6996'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Submitted Version
page: 482 - 491
publication_status: published
publisher: Springer
publist_id: '3309'
quality_controlled: '1'
status: public
title: 'What’s decidable about weighted automata '
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 6996
year: '2011'
...
---
_id: '3327'
abstract:
- lang: eng
text: We solve the open problems of translating, when possible, all common classes
of nondeterministic word automata to deterministic and nondeterministic co-Büchi
word automata. The handled classes include Büchi, parity, Rabin, Streett and Muller
automata. The translations follow a unified approach and are all asymptotically
tight. The problem of translating Büchi automata to equivalent co-Büchi automata
was solved in [2], leaving open the problems of translating automata with richer
acceptance conditions. For these classes, one cannot easily extend or use the
construction in [2]. In particular, going via an intermediate Büchi automaton
is not optimal and might involve a blow-up exponentially higher than the known
lower bound. Other known translations are also not optimal and involve a doubly
exponential blow-up. We describe direct, simple, and asymptotically tight constructions,
involving a 2Θ(n) blow-up. The constructions are variants of the subset construction,
and allow for symbolic implementations. Beyond the theoretical importance of the
results, the new constructions have various applications, among which is an improved
algorithm for translating, when possible, LTL formulas to deterministic Büchi
word automata.
alternative_title:
- LNCS
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Orna
full_name: Kupferman, Orna
last_name: Kupferman
citation:
ama: 'Boker U, Kupferman O. Co-Büching them all. In: Hofmann M, ed. Vol 6604. Springer;
2011:184-198. doi:10.1007/978-3-642-19805-2_13'
apa: 'Boker, U., & Kupferman, O. (2011). Co-Büching them all. In M. Hofmann
(Ed.) (Vol. 6604, pp. 184–198). Presented at the FoSSaCS: Foundations of Software
Science and Computation Structures, Saarbrücken, Germany: Springer. https://doi.org/10.1007/978-3-642-19805-2_13'
chicago: Boker, Udi, and Orna Kupferman. “Co-Büching Them All.” edited by Martin
Hofmann, 6604:184–98. Springer, 2011. https://doi.org/10.1007/978-3-642-19805-2_13.
ieee: 'U. Boker and O. Kupferman, “Co-Büching them all,” presented at the FoSSaCS:
Foundations of Software Science and Computation Structures, Saarbrücken, Germany,
2011, vol. 6604, pp. 184–198.'
ista: 'Boker U, Kupferman O. 2011. Co-Büching them all. FoSSaCS: Foundations of
Software Science and Computation Structures, LNCS, vol. 6604, 184–198.'
mla: Boker, Udi, and Orna Kupferman. Co-Büching Them All. Edited by Martin
Hofmann, vol. 6604, Springer, 2011, pp. 184–98, doi:10.1007/978-3-642-19805-2_13.
short: U. Boker, O. Kupferman, in:, M. Hofmann (Ed.), Springer, 2011, pp. 184–198.
conference:
end_date: 2011-04-03
location: Saarbrücken, Germany
name: 'FoSSaCS: Foundations of Software Science and Computation Structures'
start_date: 2011-03-26
date_created: 2018-12-11T12:02:41Z
date_published: 2011-03-29T00:00:00Z
date_updated: 2021-01-12T07:42:41Z
day: '29'
doi: 10.1007/978-3-642-19805-2_13
editor:
- first_name: Martin
full_name: Hofmann, Martin
last_name: Hofmann
extern: '1'
intvolume: ' 6604'
language:
- iso: eng
month: '03'
oa_version: None
page: 184 - 198
publication_status: published
publisher: Springer
publist_id: '3308'
quality_controlled: '1'
status: public
title: Co-Büching them all
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 6604
year: '2011'
...
---
_id: '3360'
abstract:
- lang: eng
text: 'A discounted-sum automaton (NDA) is a nondeterministic finite automaton with
edge weights, which values a run by the discounted sum of visited edge weights.
More precisely, the weight in the i-th position of the run is divided by lambda^i,
where the discount factor lambda is a fixed rational number greater than 1. Discounted
summation is a common and useful measuring scheme, especially for infinite sequences,
which reflects the assumption that earlier weights are more important than later
weights. Determinizing automata is often essential, for example, in formal verification,
where there are polynomial algorithms for comparing two deterministic NDAs, while
the equivalence problem for NDAs is not known to be decidable. Unfortunately,
however, discounted-sum automata are, in general, not determinizable: it is currently
known that for every rational discount factor 1 < lambda < 2, there is an
NDA with lambda (denoted lambda-NDA) that cannot be determinized. We provide positive
news, showing that every NDA with an integral factor is determinizable. We also
complete the picture by proving that the integers characterize exactly the discount
factors that guarantee determinizability: we show that for every non-integral
rational factor lambda, there is a nondeterminizable lambda-NDA. Finally, we prove
that the class of NDAs with integral discount factors enjoys closure under the
algebraic operations min, max, addition, and subtraction, which is not the case
for general NDAs nor for deterministic NDAs. This shows that for integral discount
factors, the class of NDAs forms an attractive specification formalism in quantitative
formal verification. All our results hold equally for automata over finite words
and for automata over infinite words. '
alternative_title:
- LIPIcs
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
citation:
ama: 'Boker U, Henzinger TA. Determinizing discounted-sum automata. In: Vol 12.
Springer; 2011:82-96. doi:10.4230/LIPIcs.CSL.2011.82'
apa: 'Boker, U., & Henzinger, T. A. (2011). Determinizing discounted-sum automata
(Vol. 12, pp. 82–96). Presented at the CSL: Computer Science Logic, Bergen, Norway:
Springer. https://doi.org/10.4230/LIPIcs.CSL.2011.82'
chicago: Boker, Udi, and Thomas A Henzinger. “Determinizing Discounted-Sum Automata,”
12:82–96. Springer, 2011. https://doi.org/10.4230/LIPIcs.CSL.2011.82.
ieee: 'U. Boker and T. A. Henzinger, “Determinizing discounted-sum automata,” presented
at the CSL: Computer Science Logic, Bergen, Norway, 2011, vol. 12, pp. 82–96.'
ista: 'Boker U, Henzinger TA. 2011. Determinizing discounted-sum automata. CSL:
Computer Science Logic, LIPIcs, vol. 12, 82–96.'
mla: Boker, Udi, and Thomas A. Henzinger. Determinizing Discounted-Sum Automata.
Vol. 12, Springer, 2011, pp. 82–96, doi:10.4230/LIPIcs.CSL.2011.82.
short: U. Boker, T.A. Henzinger, in:, Springer, 2011, pp. 82–96.
conference:
end_date: 2011-09-15
location: Bergen, Norway
name: 'CSL: Computer Science Logic'
start_date: 2011-09-12
date_created: 2018-12-11T12:02:53Z
date_published: 2011-08-31T00:00:00Z
date_updated: 2021-01-12T07:42:56Z
day: '31'
ddc:
- '004'
department:
- _id: ToHe
doi: 10.4230/LIPIcs.CSL.2011.82
ec_funded: 1
file:
- access_level: open_access
checksum: 250603c6be8ccad4fbd4d7b24221f0ee
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:17Z
date_updated: 2020-07-14T12:46:10Z
file_id: '4803'
file_name: IST-2012-82-v1+1_Determinizing_discounted-sum_automata.pdf
file_size: 504270
relation: main_file
file_date_updated: 2020-07-14T12:46:10Z
has_accepted_license: '1'
intvolume: ' 12'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 82 - 96
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25EFB36C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '215543'
name: COMponent-Based Embedded Systems design Techniques
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
- _id: 25F1337C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '214373'
name: Design for Embedded Systems
publication_status: published
publisher: Springer
publist_id: '3255'
pubrep_id: '82'
quality_controlled: '1'
scopus_import: 1
status: public
title: Determinizing discounted-sum automata
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12
year: '2011'
...
---
_id: '3356'
abstract:
- lang: eng
text: There is recently a significant effort to add quantitative objectives to formal
verification and synthesis. We introduce and investigate the extension of temporal
logics with quantitative atomic assertions, aiming for a general and flexible
framework for quantitative-oriented specifications. In the heart of quantitative
objectives lies the accumulation of values along a computation. It is either the
accumulated summation, as with the energy objectives, or the accumulated average,
as with the mean-payoff objectives. We investigate the extension of temporal logics
with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is
a numeric variable of the system, c is a constant rational number, and Sum(v)
and Avg(v) denote the accumulated sum and average of the values of v from the
beginning of the computation up to the current point of time. We also allow the
path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring
to the average value along an entire computation. We study the border of decidability
for extensions of various temporal logics. In particular, we show that extending
the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by
prefix-accumulation assertions and extending LTL with path-accumulation assertions,
result in temporal logics whose model-checking problem is decidable. The extended
logics allow to significantly extend the currently known energy and mean-payoff
objectives. Moreover, the prefix-accumulation assertions may be refined with "controlled-accumulation",
allowing, for example, to specify constraints on the average waiting time between
a request and a grant. On the negative side, we show that the fragment we point
to is, in a sense, the maximal logic whose extension with prefix-accumulation
assertions permits a decidable model-checking procedure. Extending a temporal
logic that has the EG or EU modalities, and in particular CTL and LTL, makes the
problem undecidable.
article_number: '5970226'
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Orna
full_name: Kupferman, Orna
last_name: Kupferman
citation:
ama: 'Boker U, Chatterjee K, Henzinger TA, Kupferman O. Temporal specifications
with accumulative values. In: IEEE; 2011. doi:10.1109/LICS.2011.33'
apa: 'Boker, U., Chatterjee, K., Henzinger, T. A., & Kupferman, O. (2011). Temporal
specifications with accumulative values. Presented at the LICS: Logic in Computer
Science, Toronto, Canada: IEEE. https://doi.org/10.1109/LICS.2011.33'
chicago: Boker, Udi, Krishnendu Chatterjee, Thomas A Henzinger, and Orna Kupferman.
“Temporal Specifications with Accumulative Values.” IEEE, 2011. https://doi.org/10.1109/LICS.2011.33.
ieee: 'U. Boker, K. Chatterjee, T. A. Henzinger, and O. Kupferman, “Temporal specifications
with accumulative values,” presented at the LICS: Logic in Computer Science, Toronto,
Canada, 2011.'
ista: 'Boker U, Chatterjee K, Henzinger TA, Kupferman O. 2011. Temporal specifications
with accumulative values. LICS: Logic in Computer Science, 5970226.'
mla: Boker, Udi, et al. Temporal Specifications with Accumulative Values.
5970226, IEEE, 2011, doi:10.1109/LICS.2011.33.
short: U. Boker, K. Chatterjee, T.A. Henzinger, O. Kupferman, in:, IEEE, 2011.
conference:
end_date: 2011-06-24
location: Toronto, Canada
name: 'LICS: Logic in Computer Science'
start_date: 2011-06-21
date_created: 2018-12-11T12:02:52Z
date_published: 2011-06-21T00:00:00Z
date_updated: 2023-02-23T12:23:54Z
day: '21'
ddc:
- '000'
- '004'
department:
- _id: ToHe
- _id: KrCh
doi: 10.1109/LICS.2011.33
ec_funded: 1
file:
- access_level: open_access
checksum: 792128f5455f0f40f1105f0398e05fa9
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:42Z
date_updated: 2020-07-14T12:46:09Z
file_id: '4960'
file_name: IST-2012-83-v1+1_Temporal_specifications_with_accumulative_values.pdf
file_size: 225426
relation: main_file
file_date_updated: 2020-07-14T12:46:09Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25EFB36C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '215543'
name: COMponent-Based Embedded Systems design Techniques
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
- _id: 25F1337C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '214373'
name: Design for Embedded Systems
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication_status: published
publisher: IEEE
publist_id: '3259'
pubrep_id: '83'
related_material:
record:
- id: '2038'
relation: later_version
status: public
- id: '5385'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Temporal specifications with accumulative values
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '5385'
abstract:
- lang: eng
text: There is recently a significant effort to add quantitative objectives to formal
verification and synthesis. We introduce and investigate the extension of temporal
logics with quantitative atomic assertions, aiming for a general and flexible
framework for quantitative-oriented specifications. In the heart of quantitative
objectives lies the accumulation of values along a computation. It is either the
accumulated summation, as with the energy objectives, or the accumulated average,
as with the mean-payoff objectives. We investigate the extension of temporal logics
with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is
a numeric variable of the system, c is a constant rational number, and Sum(v)
and Avg(v) denote the accumulated sum and average of the values of v from the
beginning of the computation up to the current point of time. We also allow the
path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring
to the average value along an entire computation. We study the border of decidability
for extensions of various temporal logics. In particular, we show that extending
the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by
prefix-accumulation assertions and extending LTL with path-accumulation assertions,
result in temporal logics whose model-checking problem is decidable. The extended
logics allow to significantly extend the currently known energy and mean-payoff
objectives. Moreover, the prefix-accumulation assertions may be refined with “controlled-accumulation”,
allowing, for example, to specify constraints on the average waiting time between
a request and a grant. On the negative side, we show that the fragment we point
to is, in a sense, the maximal logic whose extension with prefix-accumulation
assertions permits a decidable model-checking procedure. Extending a temporal
logic that has the EG or EU modalities, and in particular CTL and LTL, makes the
problem undecidable.
alternative_title:
- IST Austria Technical Report
author:
- first_name: Udi
full_name: Boker, Udi
id: 31E297B6-F248-11E8-B48F-1D18A9856A87
last_name: Boker
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Orna
full_name: Kupferman, Orna
last_name: Kupferman
citation:
ama: Boker U, Chatterjee K, Henzinger TA, Kupferman O. Temporal Specifications
with Accumulative Values. IST Austria; 2011. doi:10.15479/AT:IST-2011-0003
apa: Boker, U., Chatterjee, K., Henzinger, T. A., & Kupferman, O. (2011). Temporal
specifications with accumulative values. IST Austria. https://doi.org/10.15479/AT:IST-2011-0003
chicago: Boker, Udi, Krishnendu Chatterjee, Thomas A Henzinger, and Orna Kupferman.
Temporal Specifications with Accumulative Values. IST Austria, 2011. https://doi.org/10.15479/AT:IST-2011-0003.
ieee: U. Boker, K. Chatterjee, T. A. Henzinger, and O. Kupferman, Temporal specifications
with accumulative values. IST Austria, 2011.
ista: Boker U, Chatterjee K, Henzinger TA, Kupferman O. 2011. Temporal specifications
with accumulative values, IST Austria, 14p.
mla: Boker, Udi, et al. Temporal Specifications with Accumulative Values.
IST Austria, 2011, doi:10.15479/AT:IST-2011-0003.
short: U. Boker, K. Chatterjee, T.A. Henzinger, O. Kupferman, Temporal Specifications
with Accumulative Values, IST Austria, 2011.
date_created: 2018-12-12T11:39:02Z
date_published: 2011-04-04T00:00:00Z
date_updated: 2023-02-23T11:23:41Z
day: '04'
ddc:
- '000'
- '004'
department:
- _id: ToHe
- _id: KrCh
doi: 10.15479/AT:IST-2011-0003
ec_funded: 1
file:
- access_level: open_access
checksum: 8491d0d48c4911620ecd5350b413c11e
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:53:00Z
date_updated: 2020-07-14T12:46:41Z
file_id: '5461'
file_name: IST-2011-0003_IST-2011-0003.pdf
file_size: 366281
relation: main_file
file_date_updated: 2020-07-14T12:46:41Z
has_accepted_license: '1'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: '14'
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25EFB36C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '215543'
name: COMponent-Based Embedded Systems design Techniques
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
- _id: 25F1337C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '214373'
name: Design for Embedded Systems
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '21'
related_material:
record:
- id: '2038'
relation: later_version
status: public
- id: '3356'
relation: later_version
status: public
status: public
title: Temporal specifications with accumulative values
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2011'
...