Article

Power of Randomization in Automata on Infinite Strings

Authors:

A. Prasad Sistla,

Mahesh ViswanathanAuthors Info & Claims

CONCUR 2009: Proceedings of the 20th International Conference on Concurrency Theory

Pages 229 - 243

https://doi.org/10.1007/978-3-642-04081-8_16

Published: 01 September 2009 Publication History

Abstract

Probabilistic Büchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this paper, we present a number of results that clarify the power of such machines and properties of the languages they define. The broad themes we focus on are as follows. We precisely characterize the complexity of the emptiness, universality, and language containment problems for such machines, answering canonical questions central to the use of these models in formal verification. Next, we characterize the languages recognized by PBAs topologically, demonstrating that though general PBAs can recognize languages that are not regular, topologically the languages are as simple as <em>***</em> -regular languages. Finally, we introduce Hierarchical PBAs, which are syntactically restricted forms of PBAs that are tractable and capture exactly the class of <em>***</em> -regular languages.

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Cited By

Chadha RSistla AViswanathan M(2017)Emptiness Under Isolation and the Value Problem for Hierarchical Probabilistic AutomataProceedings of the 20th International Conference on Foundations of Software Science and Computation Structures - Volume 1020310.1007/978-3-662-54458-7_14(231-247)Online publication date: 22-Apr-2017
https://dl.acm.org/doi/10.1007/978-3-662-54458-7_14
Carayol AHaddad ASerre O(2014)Randomization in Automata on Infinite TreesACM Transactions on Computational Logic10.1145/262933615:3(1-33)Online publication date: 17-Jul-2014
https://dl.acm.org/doi/10.1145/2629336
Chatterjee KDoyen L(2014)Partial-Observation Stochastic GamesACM Transactions on Computational Logic10.1145/257982115:2(1-44)Online publication date: 2-May-2014
https://dl.acm.org/doi/10.1145/2579821
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Power of Randomization in Automata on Infinite Strings
1. Software and its engineering
  1. Software notations and tools
2. Theory of computation

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Information

Published In

cover image Guide Proceedings

CONCUR 2009: Proceedings of the 20th International Conference on Concurrency Theory

September 2009

636 pages

ISBN:9783642040801

Editors:
Mario Bravetti
Department of Computer Science, University of Bologna, Bologna, Italy 40127
,
Gianluigi Zavattaro
Department of Computer Science, University of Bologna, Bologna, Italy 40127

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 September 2009

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Cited By

Chadha RSistla AViswanathan M(2017)Emptiness Under Isolation and the Value Problem for Hierarchical Probabilistic AutomataProceedings of the 20th International Conference on Foundations of Software Science and Computation Structures - Volume 1020310.1007/978-3-662-54458-7_14(231-247)Online publication date: 22-Apr-2017
https://dl.acm.org/doi/10.1007/978-3-662-54458-7_14
Carayol AHaddad ASerre O(2014)Randomization in Automata on Infinite TreesACM Transactions on Computational Logic10.1145/262933615:3(1-33)Online publication date: 17-Jul-2014
https://dl.acm.org/doi/10.1145/2629336
Chatterjee KDoyen L(2014)Partial-Observation Stochastic GamesACM Transactions on Computational Logic10.1145/257982115:2(1-44)Online publication date: 2-May-2014
https://dl.acm.org/doi/10.1145/2579821
Weidner T(2014)Probabilistic ω-Regular ExpressionsProceedings of the 8th International Conference on Language and Automata Theory and Applications - Volume 837010.1007/978-3-319-04921-2_48(588-600)Online publication date: 10-Mar-2014
https://dl.acm.org/doi/10.1007/978-3-319-04921-2_48
Baier CGrösser MBertrand N(2012)Probabilistic ω-automataJournal of the ACM10.1145/2108242.210824359:1(1-52)Online publication date: 2-Mar-2012
https://dl.acm.org/doi/10.1145/2108242.2108243
Fijalkow NGimbert HOualhadj Y(2012)Deciding the Value 1 Problem for Probabilistic Leaktight AutomataProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.40(295-304)Online publication date: 25-Jun-2012
https://dl.acm.org/doi/10.1109/LICS.2012.40
Chatterjee KTracol M(2012)Decidable Problems for Probabilistic Automata on Infinite WordsProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.29(185-194)Online publication date: 25-Jun-2012
https://dl.acm.org/doi/10.1109/LICS.2012.29
Chatterjee KDoyen L(2012)Partial-Observation Stochastic GamesProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.28(175-184)Online publication date: 25-Jun-2012
https://dl.acm.org/doi/10.1109/LICS.2012.28
Weidner T(2012)Probabilistic automata and probabilistic logicProceedings of the 37th international conference on Mathematical Foundations of Computer Science10.1007/978-3-642-32589-2_70(813-824)Online publication date: 27-Aug-2012
https://dl.acm.org/doi/10.1007/978-3-642-32589-2_70
Chadha RSistla AViswanathan M(2011)Probabilistic Büchi automata with non-extremal acceptance thresholdsProceedings of the 12th international conference on Verification, model checking, and abstract interpretation10.5555/1946284.1946293(103-117)Online publication date: 23-Jan-2011
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