---
_id: '1477'
abstract:
- lang: eng
text: We consider partially observable Markov decision processes (POMDPs) with ω-regular
conditions specified as parity objectives. The class of ω-regular languages provides
a robust specification language to express properties in verification, and parity
objectives are canonical forms to express them. The qualitative analysis problem
given a POMDP and a parity objective asks whether there is a strategy to ensure
that the objective is satisfied with probability 1 (resp. positive probability).
While the qualitative analysis problems are undecidable even for special cases
of parity objectives, we establish decidability (with optimal complexity) for
POMDPs with all parity objectives under finite-memory strategies. We establish
optimal (exponential) memory bounds and EXPTIME-completeness of the qualitative
analysis problems under finite-memory strategies for POMDPs with parity objectives.
We also present a practical approach, where we design heuristics to deal with
the exponential complexity, and have applied our implementation on a number of
POMDP examples.
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Martin
full_name: Chmelik, Martin
id: 3624234E-F248-11E8-B48F-1D18A9856A87
last_name: Chmelik
- first_name: Mathieu
full_name: Tracol, Mathieu
id: 3F54FA38-F248-11E8-B48F-1D18A9856A87
last_name: Tracol
citation:
ama: Chatterjee K, Chmelik M, Tracol M. What is decidable about partially observable
Markov decision processes with ω-regular objectives. Journal of Computer and
System Sciences. 2016;82(5):878-911. doi:10.1016/j.jcss.2016.02.009
apa: Chatterjee, K., Chmelik, M., & Tracol, M. (2016). What is decidable about
partially observable Markov decision processes with ω-regular objectives. Journal
of Computer and System Sciences. Elsevier. https://doi.org/10.1016/j.jcss.2016.02.009
chicago: Chatterjee, Krishnendu, Martin Chmelik, and Mathieu Tracol. “What Is Decidable
about Partially Observable Markov Decision Processes with ω-Regular Objectives.”
Journal of Computer and System Sciences. Elsevier, 2016. https://doi.org/10.1016/j.jcss.2016.02.009.
ieee: K. Chatterjee, M. Chmelik, and M. Tracol, “What is decidable about partially
observable Markov decision processes with ω-regular objectives,” Journal of
Computer and System Sciences, vol. 82, no. 5. Elsevier, pp. 878–911, 2016.
ista: Chatterjee K, Chmelik M, Tracol M. 2016. What is decidable about partially
observable Markov decision processes with ω-regular objectives. Journal of Computer
and System Sciences. 82(5), 878–911.
mla: Chatterjee, Krishnendu, et al. “What Is Decidable about Partially Observable
Markov Decision Processes with ω-Regular Objectives.” Journal of Computer and
System Sciences, vol. 82, no. 5, Elsevier, 2016, pp. 878–911, doi:10.1016/j.jcss.2016.02.009.
short: K. Chatterjee, M. Chmelik, M. Tracol, Journal of Computer and System Sciences
82 (2016) 878–911.
date_created: 2018-12-11T11:52:15Z
date_published: 2016-08-01T00:00:00Z
date_updated: 2023-02-23T12:24:38Z
day: '01'
department:
- _id: KrCh
doi: 10.1016/j.jcss.2016.02.009
ec_funded: 1
external_id:
arxiv:
- '1309.2802'
intvolume: ' 82'
issue: '5'
language:
- iso: eng
main_file_link:
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url: https://arxiv.org/abs/1309.2802
month: '08'
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oa_version: Preprint
page: 878 - 911
project:
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publisher: Elsevier
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title: What is decidable about partially observable Markov decision processes with
ω-regular objectives
type: journal_article
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volume: 82
year: '2016'
...
---
_id: '2295'
abstract:
- lang: eng
text: We consider partially observable Markov decision processes (POMDPs) with ω-regular
conditions specified as parity objectives. The qualitative analysis problem given
a POMDP and a parity objective asks whether there is a strategy to ensure that
the objective is satisfied with probability 1 (resp. positive probability). While
the qualitative analysis problems are known to be undecidable even for very special
cases of parity objectives, we establish decidability (with optimal EXPTIME-complete
complexity) of the qualitative analysis problems for POMDPs with all parity objectives
under finite-memory strategies. We also establish asymptotically optimal (exponential)
memory bounds.
alternative_title:
- LIPIcs
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Martin
full_name: Chmelik, Martin
id: 3624234E-F248-11E8-B48F-1D18A9856A87
last_name: Chmelik
- first_name: Mathieu
full_name: Tracol, Mathieu
id: 3F54FA38-F248-11E8-B48F-1D18A9856A87
last_name: Tracol
citation:
ama: Chatterjee K, Chmelik M, Tracol M. What is decidable about partially observable
Markov decision processes with omega-regular objectives. 2013;23:165-180. doi:10.4230/LIPIcs.CSL.2013.165
apa: 'Chatterjee, K., Chmelik, M., & Tracol, M. (2013). What is decidable about
partially observable Markov decision processes with omega-regular objectives.
Presented at the CSL: Computer Science Logic, Torino, Italy: Schloss Dagstuhl
- Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.CSL.2013.165'
chicago: Chatterjee, Krishnendu, Martin Chmelik, and Mathieu Tracol. “What Is Decidable
about Partially Observable Markov Decision Processes with Omega-Regular Objectives.”
Leibniz International Proceedings in Informatics. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2013. https://doi.org/10.4230/LIPIcs.CSL.2013.165.
ieee: K. Chatterjee, M. Chmelik, and M. Tracol, “What is decidable about partially
observable Markov decision processes with omega-regular objectives,” vol. 23.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, pp. 165–180, 2013.
ista: Chatterjee K, Chmelik M, Tracol M. 2013. What is decidable about partially
observable Markov decision processes with omega-regular objectives. 23, 165–180.
mla: Chatterjee, Krishnendu, et al. What Is Decidable about Partially Observable
Markov Decision Processes with Omega-Regular Objectives. Vol. 23, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2013, pp. 165–80, doi:10.4230/LIPIcs.CSL.2013.165.
short: K. Chatterjee, M. Chmelik, M. Tracol, 23 (2013) 165–180.
conference:
end_date: 2013-09-05
location: Torino, Italy
name: 'CSL: Computer Science Logic'
start_date: 2013-09-02
date_created: 2018-12-11T11:56:50Z
date_published: 2013-08-27T00:00:00Z
date_updated: 2023-02-23T12:24:38Z
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ddc:
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department:
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doi: 10.4230/LIPIcs.CSL.2013.165
ec_funded: 1
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related_material:
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scopus_import: 1
series_title: Leibniz International Proceedings in Informatics
status: public
title: What is decidable about partially observable Markov decision processes with
omega-regular objectives
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abstract:
- lang: eng
text: We consider partially observable Markov decision processes (POMDPs) with ω-regular
conditions specified as parity objectives. The class of ω-regular languages extends
regular languages to infinite strings and provides a robust specification language
to express all properties used in verification, and parity objectives are canonical
forms to express ω-regular conditions. The qualitative analysis problem given
a POMDP and a parity objective asks whether there is a strategy to ensure that
the objective is satis- fied with probability 1 (resp. positive probability).
While the qualitative analysis problems are known to be undecidable even for very
special cases of parity objectives, we establish decidability (with optimal complexity)
of the qualitative analysis problems for POMDPs with all parity objectives under
finite- memory strategies. We establish asymptotically optimal (exponential) memory
bounds and EXPTIME- completeness of the qualitative analysis problems under finite-memory
strategies for POMDPs with parity objectives.
alternative_title:
- IST Austria Technical Report
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Martin
full_name: Chmelik, Martin
id: 3624234E-F248-11E8-B48F-1D18A9856A87
last_name: Chmelik
- first_name: Mathieu
full_name: Tracol, Mathieu
id: 3F54FA38-F248-11E8-B48F-1D18A9856A87
last_name: Tracol
citation:
ama: Chatterjee K, Chmelik M, Tracol M. What Is Decidable about Partially Observable
Markov Decision Processes with ω-Regular Objectives. IST Austria; 2013. doi:10.15479/AT:IST-2013-109-v1-1
apa: Chatterjee, K., Chmelik, M., & Tracol, M. (2013). What is decidable
about partially observable Markov decision processes with ω-regular objectives.
IST Austria. https://doi.org/10.15479/AT:IST-2013-109-v1-1
chicago: Chatterjee, Krishnendu, Martin Chmelik, and Mathieu Tracol. What Is
Decidable about Partially Observable Markov Decision Processes with ω-Regular
Objectives. IST Austria, 2013. https://doi.org/10.15479/AT:IST-2013-109-v1-1.
ieee: K. Chatterjee, M. Chmelik, and M. Tracol, What is decidable about partially
observable Markov decision processes with ω-regular objectives. IST Austria,
2013.
ista: Chatterjee K, Chmelik M, Tracol M. 2013. What is decidable about partially
observable Markov decision processes with ω-regular objectives, IST Austria, 41p.
mla: Chatterjee, Krishnendu, et al. What Is Decidable about Partially Observable
Markov Decision Processes with ω-Regular Objectives. IST Austria, 2013, doi:10.15479/AT:IST-2013-109-v1-1.
short: K. Chatterjee, M. Chmelik, M. Tracol, What Is Decidable about Partially Observable
Markov Decision Processes with ω-Regular Objectives, IST Austria, 2013.
date_created: 2018-12-12T11:39:07Z
date_published: 2013-02-20T00:00:00Z
date_updated: 2023-02-23T10:36:45Z
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publication_identifier:
issn:
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publication_status: published
publisher: IST Austria
pubrep_id: '109'
related_material:
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relation: later_version
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status: public
title: What is decidable about partially observable Markov decision processes with
ω-regular objectives
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2957'
abstract:
- lang: eng
text: 'We consider probabilistic automata on infinite words with acceptance defined
by parity conditions. We consider three qualitative decision problems: (i) the
positive decision problem asks whether there is a word that is accepted with positive
probability; (ii) the almost decision problem asks whether there is a word that
is accepted with probability 1; and (iii) the limit decision problem asks whether
words are accepted with probability arbitrarily close to 1. We unify and generalize
several decidability results for probabilistic automata over infinite words, and
identify a robust (closed under union and intersection) subclass of probabilistic
automata for which all the qualitative decision problems are decidable for parity
conditions. We also show that if the input words are restricted to lasso shape
(regular) words, then the positive and almost problems are decidable for all probabilistic
automata with parity conditions. For most decidable problems we show an optimal
PSPACE-complete complexity bound.'
article_number: '6280437'
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Mathieu
full_name: Tracol, Mathieu
id: 3F54FA38-F248-11E8-B48F-1D18A9856A87
last_name: Tracol
citation:
ama: 'Chatterjee K, Tracol M. Decidable problems for probabilistic automata on infinite
words. In: Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic
in Computer Science. IEEE; 2012. doi:10.1109/LICS.2012.29'
apa: 'Chatterjee, K., & Tracol, M. (2012). Decidable problems for probabilistic
automata on infinite words. In Proceedings of the 2012 27th Annual ACM/IEEE
Symposium on Logic in Computer Science. Dubrovnik, Croatia : IEEE. https://doi.org/10.1109/LICS.2012.29'
chicago: Chatterjee, Krishnendu, and Mathieu Tracol. “Decidable Problems for Probabilistic
Automata on Infinite Words.” In Proceedings of the 2012 27th Annual ACM/IEEE
Symposium on Logic in Computer Science. IEEE, 2012. https://doi.org/10.1109/LICS.2012.29.
ieee: K. Chatterjee and M. Tracol, “Decidable problems for probabilistic automata
on infinite words,” in Proceedings of the 2012 27th Annual ACM/IEEE Symposium
on Logic in Computer Science, Dubrovnik, Croatia , 2012.
ista: 'Chatterjee K, Tracol M. 2012. Decidable problems for probabilistic automata
on infinite words. Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic
in Computer Science. LICS: Logic in Computer Science, 6280437.'
mla: Chatterjee, Krishnendu, and Mathieu Tracol. “Decidable Problems for Probabilistic
Automata on Infinite Words.” Proceedings of the 2012 27th Annual ACM/IEEE Symposium
on Logic in Computer Science, 6280437, IEEE, 2012, doi:10.1109/LICS.2012.29.
short: K. Chatterjee, M. Tracol, in:, Proceedings of the 2012 27th Annual ACM/IEEE
Symposium on Logic in Computer Science, IEEE, 2012.
conference:
end_date: 2012-06-28
location: 'Dubrovnik, Croatia '
name: 'LICS: Logic in Computer Science'
start_date: 2012-06-25
date_created: 2018-12-11T12:00:33Z
date_published: 2012-08-23T00:00:00Z
date_updated: 2023-02-23T12:23:51Z
day: '23'
department:
- _id: KrCh
doi: 10.1109/LICS.2012.29
ec_funded: 1
external_id:
arxiv:
- '1107.2091'
language:
- iso: eng
main_file_link:
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url: https://arxiv.org/abs/1107.2091
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
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grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
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name: Microsoft Research Faculty Fellowship
publication: Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer
Science
publication_status: published
publisher: IEEE
publist_id: '3769'
quality_controlled: '1'
related_material:
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relation: earlier_version
status: public
scopus_import: 1
status: public
title: Decidable problems for probabilistic automata on infinite words
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2012'
...
---
_id: '3363'
abstract:
- lang: eng
text: We consider probabilistic automata on infinite words with acceptance defined
by safety, reachability, Büchi, coBüchi, and limit-average conditions. We consider
quantitative and qualitative decision problems. We present extensions and adaptations
of proofs for probabilistic finite automata and present a complete characterization
of the decidability and undecidability frontier of the quantitative and qualitative
decision problems for probabilistic automata on infinite words.
author:
- 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: Mathieu
full_name: Tracol, Mathieu
id: 3F54FA38-F248-11E8-B48F-1D18A9856A87
last_name: Tracol
citation:
ama: Chatterjee K, Henzinger TA, Tracol M. The decidability frontier for probabilistic
automata on infinite words.
apa: Chatterjee, K., Henzinger, T. A., & Tracol, M. (n.d.). The decidability
frontier for probabilistic automata on infinite words. ArXiv.
chicago: Chatterjee, Krishnendu, Thomas A Henzinger, and Mathieu Tracol. “The Decidability
Frontier for Probabilistic Automata on Infinite Words.” ArXiv, n.d.
ieee: K. Chatterjee, T. A. Henzinger, and M. Tracol, “The decidability frontier
for probabilistic automata on infinite words.” ArXiv.
ista: Chatterjee K, Henzinger TA, Tracol M. The decidability frontier for probabilistic
automata on infinite words.
mla: Chatterjee, Krishnendu, et al. The Decidability Frontier for Probabilistic
Automata on Infinite Words. ArXiv.
short: K. Chatterjee, T.A. Henzinger, M. Tracol, (n.d.).
date_created: 2018-12-11T12:02:54Z
date_published: 2011-04-01T00:00:00Z
date_updated: 2020-01-21T13:20:24Z
day: '01'
department:
- _id: KrCh
- _id: ToHe
ec_funded: 1
external_id:
arxiv:
- '1104.0127'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1104.0127
month: '04'
oa: 1
oa_version: Preprint
page: '19'
project:
- _id: 25EFB36C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '215543'
name: COMponent-Based Embedded Systems design Techniques
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call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
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call_identifier: FP7
grant_number: '214373'
name: Design for Embedded Systems
publication_status: submitted
publisher: ArXiv
publist_id: '3251'
status: public
title: The decidability frontier for probabilistic automata on infinite words
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2011'
...
---
_id: '5384'
abstract:
- lang: eng
text: 'We consider probabilistic automata on infinite words with acceptance defined
by parity conditions. We consider three qualitative decision problems: (i) the
positive decision problem asks whether there is a word that is accepted with positive
probability; (ii) the almost decision problem asks whether there is a word that
is accepted with probability 1; and (iii) the limit decision problem asks whether
for every ε > 0 there is a word that is accepted with probability at least 1 −
ε. We unify and generalize several decidability results for probabilistic automata
over infinite words, and identify a robust (closed under union and intersection)
subclass of probabilistic automata for which all the qualitative decision problems
are decidable for parity conditions. We also show that if the input words are
restricted to lasso shape words, then the positive and almost problems are decidable
for all probabilistic automata with parity conditions.'
alternative_title:
- IST Austria Technical Report
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Mathieu
full_name: Tracol, Mathieu
id: 3F54FA38-F248-11E8-B48F-1D18A9856A87
last_name: Tracol
citation:
ama: Chatterjee K, Tracol M. Decidable Problems for Probabilistic Automata on
Infinite Words. IST Austria; 2011. doi:10.15479/AT:IST-2011-0004
apa: Chatterjee, K., & Tracol, M. (2011). Decidable problems for probabilistic
automata on infinite words. IST Austria. https://doi.org/10.15479/AT:IST-2011-0004
chicago: Chatterjee, Krishnendu, and Mathieu Tracol. Decidable Problems for Probabilistic
Automata on Infinite Words. IST Austria, 2011. https://doi.org/10.15479/AT:IST-2011-0004.
ieee: K. Chatterjee and M. Tracol, Decidable problems for probabilistic automata
on infinite words. IST Austria, 2011.
ista: Chatterjee K, Tracol M. 2011. Decidable problems for probabilistic automata
on infinite words, IST Austria, 30p.
mla: Chatterjee, Krishnendu, and Mathieu Tracol. Decidable Problems for Probabilistic
Automata on Infinite Words. IST Austria, 2011, doi:10.15479/AT:IST-2011-0004.
short: K. Chatterjee, M. Tracol, Decidable Problems for Probabilistic Automata on
Infinite Words, IST Austria, 2011.
date_created: 2018-12-12T11:39:01Z
date_published: 2011-04-11T00:00:00Z
date_updated: 2023-02-23T11:05:53Z
day: '11'
ddc:
- '000'
- '005'
department:
- _id: KrCh
doi: 10.15479/AT:IST-2011-0004
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title: Decidable problems for probabilistic automata on infinite words
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