---
_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
arxiv: 1
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
corr_author: '1'
date_created: 2023-07-14T10:00:15Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2026-04-07T12:02:57Z
day: '01'
ddc:
- '000'
department:
- _id: GradSch
- _id: ToHe
doi: 10.4230/LIPIcs.CONCUR.2023.17
ec_funded: 1
external_id:
arxiv:
- '2307.06016'
isi:
- '001570542500017'
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'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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'
related_material:
record:
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relation: dissertation_contains
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scopus_import: '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
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...