---
_id: '10002'
abstract:
- lang: eng
text: 'We present a faster symbolic algorithm for the following central problem
in probabilistic verification: Compute the maximal end-component (MEC) decomposition
of Markov decision processes (MDPs). This problem generalizes the SCC decomposition
problem of graphs and closed recurrent sets of Markov chains. The model of symbolic
algorithms is widely used in formal verification and model-checking, where access
to the input model is restricted to only symbolic operations (e.g., basic set
operations and computation of one-step neighborhood). For an input MDP with n vertices
and m edges, the classical symbolic algorithm from the 1990s for the MEC decomposition
requires O(n2) symbolic operations and O(1) symbolic space. The only other
symbolic algorithm for the MEC decomposition requires O(nm−−√) symbolic operations
and O(m−−√) symbolic space. A main open question is whether the worst-case O(n2) bound
for symbolic operations can be beaten. We present a symbolic algorithm that requires O˜(n1.5) symbolic
operations and O˜(n−−√) symbolic space. Moreover, the parametrization of our
algorithm provides a trade-off between symbolic operations and symbolic space:
for all 0<ϵ≤1/2 the symbolic algorithm requires O˜(n2−ϵ) symbolic operations
and O˜(nϵ) symbolic space ( O˜ hides poly-logarithmic factors). Using our techniques
we present faster algorithms for computing the almost-sure winning regions of ω
-regular objectives for MDPs. We consider the canonical parity objectives for ω
-regular objectives, and for parity objectives with d -priorities we present
an algorithm that computes the almost-sure winning region with O˜(n2−ϵ) symbolic
operations and O˜(nϵ) symbolic space, for all 0<ϵ≤1/2 .'
acknowledgement: The authors are grateful to the anonymous referees for their valuable
comments. A. S. is fully supported by the Vienna Science and Technology Fund (WWTF)
through project ICT15–003. K. C. is supported by the Austrian Science Fund (FWF)
NFN Grant No S11407-N23 (RiSE/SHiNE) and by the ERC CoG 863818 (ForM-SMArt). For
M. H. the research leading to these results has received funding from the European
Research Council under the European Unions Seventh Framework Programme (FP/2007–2013)
/ ERC Grant Agreement no. 340506.
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Wolfgang
full_name: Dvorak, Wolfgang
last_name: Dvorak
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Alexander
full_name: Svozil, Alexander
last_name: Svozil
citation:
ama: 'Chatterjee K, Dvorak W, Henzinger MH, Svozil A. Symbolic time and space tradeoffs
for probabilistic verification. In: Proceedings of the 36th Annual ACM/IEEE
Symposium on Logic in Computer Science. Institute of Electrical and Electronics
Engineers; 2021:1-13. doi:10.1109/LICS52264.2021.9470739'
apa: 'Chatterjee, K., Dvorak, W., Henzinger, M. H., & Svozil, A. (2021). Symbolic
time and space tradeoffs for probabilistic verification. In Proceedings of
the 36th Annual ACM/IEEE Symposium on Logic in Computer Science (pp. 1–13).
Rome, Italy: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/LICS52264.2021.9470739'
chicago: Chatterjee, Krishnendu, Wolfgang Dvorak, Monika H Henzinger, and Alexander
Svozil. “Symbolic Time and Space Tradeoffs for Probabilistic Verification.” In
Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science,
1–13. Institute of Electrical and Electronics Engineers, 2021. https://doi.org/10.1109/LICS52264.2021.9470739.
ieee: K. Chatterjee, W. Dvorak, M. H. Henzinger, and A. Svozil, “Symbolic time and
space tradeoffs for probabilistic verification,” in Proceedings of the 36th
Annual ACM/IEEE Symposium on Logic in Computer Science, Rome, Italy, 2021,
pp. 1–13.
ista: 'Chatterjee K, Dvorak W, Henzinger MH, Svozil A. 2021. Symbolic time and space
tradeoffs for probabilistic verification. Proceedings of the 36th Annual ACM/IEEE
Symposium on Logic in Computer Science. LICS: Symposium on Logic in Computer Science,
1–13.'
mla: Chatterjee, Krishnendu, et al. “Symbolic Time and Space Tradeoffs for Probabilistic
Verification.” Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in
Computer Science, Institute of Electrical and Electronics Engineers, 2021,
pp. 1–13, doi:10.1109/LICS52264.2021.9470739.
short: K. Chatterjee, W. Dvorak, M.H. Henzinger, A. Svozil, in:, Proceedings of
the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Institute of
Electrical and Electronics Engineers, 2021, pp. 1–13.
conference:
end_date: 2021-07-02
location: Rome, Italy
name: 'LICS: Symposium on Logic in Computer Science'
start_date: 2021-06-29
date_created: 2021-09-12T22:01:24Z
date_published: 2021-07-07T00:00:00Z
date_updated: 2023-08-14T06:51:33Z
day: '07'
department:
- _id: KrCh
doi: 10.1109/LICS52264.2021.9470739
ec_funded: 1
external_id:
arxiv:
- '2104.07466'
isi:
- '000947350400089'
isi: 1
keyword:
- Computer science
- Computational modeling
- Markov processes
- Probabilistic logic
- Formal verification
- Game Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2104.07466
month: '07'
oa: 1
oa_version: Preprint
page: 1-13
project:
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer
Science
publication_identifier:
eisbn:
- 978-1-6654-4895-6
isbn:
- 978-1-6654-4896-3
issn:
- 1043-6871
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Symbolic time and space tradeoffs for probabilistic verification
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...