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A Probabilistic Kleene Theorem

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Book cover Automated Technology for Verification and Analysis (ATVA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7561))

Abstract

We provide a Kleene Theorem for (Rabin) probabilistic automata over finite words. Probabilistic automata generalize deterministic finite automata and assign to a word an acceptance probability. We provide probabilistic expressions with probabilistic choice, guarded choice, concatenation, and a star operator. We prove that probabilistic expressions and probabilistic automata are expressively equivalent. Our result actually extends to two-way probabilistic automata with pebbles and corresponding expressions.

Supported by anr 2010 blan 0202 01 frec, LIA InForMel.

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Author information

Authors and Affiliations

  1. LSV, ENS Cachan, CNRS & Inria, France

    Benedikt Bollig, Paul Gastin & Benjamin Monmege

  2. LaBRI, Univ. Bordeaux & CNRS, France

    Marc Zeitoun

Authors
  1. Benedikt Bollig
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  2. Paul Gastin
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  3. Benjamin Monmege
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  4. Marc Zeitoun
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Editor information

Editors and Affiliations

  1. Indian Institute of Technology, Computer Science and Engineering, Dept. of Computer Science and Engineering, IIT Bombay, Powai, 400076, Mumbai, Maharashtra, India

    Supratik Chakraborty

  2. Chennai Mathematical Institute, H1, SIPCOT IT Park, Kelambakkam, 603103, Siruseri, Tamil Nadu, India

    Madhavan Mukund

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Bollig, B., Gastin, P., Monmege, B., Zeitoun, M. (2012). A Probabilistic Kleene Theorem. In: Chakraborty, S., Mukund, M. (eds) Automated Technology for Verification and Analysis. ATVA 2012. Lecture Notes in Computer Science, vol 7561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33386-6_31

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  • DOI: https://doi.org/10.1007/978-3-642-33386-6_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33385-9

  • Online ISBN: 978-3-642-33386-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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