---
_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
full_name: Henzinger, Monika
last_name: Henzinger
- first_name: Alexander
full_name: Svozil, Alexander
last_name: Svozil
citation:
ama: 'Chatterjee K, Dvorak W, Henzinger M, 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., & 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 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. 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 M, 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. 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: 2021-09-16T12:19:51Z
day: '07'
department:
- _id: KrCh
doi: 10.1109/LICS52264.2021.9470739
ec_funded: 1
external_id:
arxiv:
- '2104.07466'
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '10004'
abstract:
- lang: eng
text: 'Markov chains are the de facto finite-state model for stochastic dynamical
systems, and Markov decision processes (MDPs) extend Markov chains by incorporating
non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization
criterion is the maximal expected total reward where the MDP stops after T steps,
which can be computed by a simple dynamic programming algorithm. We consider a
natural generalization of the problem where the stopping times can be chosen according
to a probability distribution, such that the expected stopping time is T, to optimize
the expected total reward. Quite surprisingly we establish inter-reducibility
of the expected stopping-time problem for Markov chains with the Positivity problem
(which is related to the well-known Skolem problem), for which establishing either
decidability or undecidability would be a major breakthrough. Given the hardness
of the exact problem, we consider the approximate version of the problem: we show
that it can be solved in exponential time for Markov chains and in exponential
space for MDPs.'
acknowledgement: We are grateful to the anonymous reviewers of LICS 2021 and of a
previous version of this paper for insightful comments that helped improving the
presentation. This research was partially supported by the grant ERC CoG 863818
(ForM-SMArt).
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: Laurent
full_name: Doyen, Laurent
last_name: Doyen
citation:
ama: 'Chatterjee K, Doyen L. Stochastic processes with expected stopping time. 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/LICS52264.2021.9470595'
apa: 'Chatterjee, K., & Doyen, L. (2021). Stochastic processes with expected
stopping time. 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/LICS52264.2021.9470595'
chicago: Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected
Stopping Time.” 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/LICS52264.2021.9470595.
ieee: K. Chatterjee and L. Doyen, “Stochastic processes with expected stopping time,”
in *Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science*,
Rome, Italy, 2021, pp. 1–13.
ista: 'Chatterjee K, Doyen L. 2021. Stochastic processes with expected stopping
time. 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, and Laurent Doyen. “Stochastic Processes with Expected
Stopping Time.” *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/LICS52264.2021.9470595.
short: K. Chatterjee, L. Doyen, 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: 2021-09-12T22:01:25Z
date_published: 2021-07-07T00:00:00Z
date_updated: 2021-09-16T12:19:56Z
day: '07'
department:
- _id: KrCh
doi: 10.1109/LICS52264.2021.9470595
ec_funded: 1
external_id:
arxiv:
- '2104.07278'
keyword:
- Computer science
- Heuristic algorithms
- Memory management
- Automata
- Markov processes
- Probability distribution
- Complexity theory
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2104.07278
month: '07'
oa: 1
oa_version: Preprint
page: 1-13
project:
- _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: Stochastic processes with expected stopping time
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '4519'
abstract:
- lang: eng
text: We summarize several recent results about hybrid automata. Our goal is to
demonstrate that concepts from the theory of discrete concurrent systems can give
insights into partly continuous systems, and that methods for the verification
of finite-state systems can be used to analyze certain systems with uncountable
state spaces
article_processing_charge: No
author:
- 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: 'Henzinger TA. The theory of hybrid automata. In: *Proceedings 11th Annual
IEEE Symposium on Logic in Computer Science*. IEEE; 1996:278-292. doi:10.1109/LICS.1996.561342 '
apa: 'Henzinger, T. A. (1996). The theory of hybrid automata. In *Proceedings
11th Annual IEEE Symposium on Logic in Computer Science* (pp. 278–292). New
Brunswick, NJ, United States of America: IEEE. https://doi.org/10.1109/LICS.1996.561342 '
chicago: Henzinger, Thomas A. “The Theory of Hybrid Automata.” In *Proceedings
11th Annual IEEE Symposium on Logic in Computer Science*, 278–92. IEEE, 1996.
https://doi.org/10.1109/LICS.1996.561342
.
ieee: T. A. Henzinger, “The theory of hybrid automata,” in *Proceedings 11th Annual
IEEE Symposium on Logic in Computer Science*, New Brunswick, NJ, United States
of America, 1996, pp. 278–292.
ista: 'Henzinger TA. 1996. The theory of hybrid automata. Proceedings 11th Annual
IEEE Symposium on Logic in Computer Science. LICS: Logic in Computer Science,
278–292.'
mla: Henzinger, Thomas A. “The Theory of Hybrid Automata.” *Proceedings 11th Annual
IEEE Symposium on Logic in Computer Science*, IEEE, 1996, pp. 278–92, doi:10.1109/LICS.1996.561342 .
short: T.A. Henzinger, in:, Proceedings 11th Annual IEEE Symposium on Logic in Computer
Science, IEEE, 1996, pp. 278–292.
conference:
end_date: 1996-07-30
location: New Brunswick, NJ, United States of America
name: 'LICS: Logic in Computer Science'
start_date: 1996-07-27
date_created: 2018-12-11T12:09:16Z
date_published: 1996-01-01T00:00:00Z
date_updated: 2022-07-06T07:56:28Z
day: '01'
doi: '10.1109/LICS.1996.561342 '
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://ieeexplore.ieee.org/document/561342
month: '01'
oa_version: None
page: 278 - 292
publication: Proceedings 11th Annual IEEE Symposium on Logic in Computer Science
publication_identifier:
issn:
- 1043-6871
publication_status: published
publisher: IEEE
publist_id: '213'
quality_controlled: '1'
status: public
title: The theory of hybrid automata
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1996'
...