A Probabilistic Kleene Theorem

  • Benedikt Bollig
  • Paul Gastin
  • Benjamin Monmege
  • Marc Zeitoun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7561)


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.


Probabilistic Choice Star Operator Probabilistic Expression Deterministic Finite Automaton XPath Query 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Benedikt Bollig
    • 1
  • Paul Gastin
    • 1
  • Benjamin Monmege
    • 1
  • Marc Zeitoun
    • 2
  1. 1.LSV, ENS Cachan, CNRS & InriaFrance
  2. 2.LaBRIUniv. Bordeaux & CNRSFrance

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