Convex Language Semantics for Nondeterministic Probabilistic Automata

  • Gerco van Heerdt
  • Justin HsuEmail author
  • Joël Ouaknine
  • Alexandra Silva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11187)


We explore language semantics for automata combining probabilistic and nondeterministic behaviors. We first show that there are precisely two natural semantics for probabilistic automata with nondeterminism. For both choices, we show that these automata are strictly more expressive than deterministic probabilistic automata, and we prove that the problem of checking language equivalence is undecidable by reduction from the threshold problem. However, we provide a discounted metric that can be computed to arbitrarily high precision.


Deterministic Probabilistic Automata Language Semantics Checking Language Equivalence Threshold Problem Linear Recurrence Sequences (LRS) 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Nathanaël Fijalkow and the anonymous reviewers for their useful suggestions to improve the paper. The semantics studied in this paper has been brought to our attention in personal communication by Filippo Bonchi, Ana Sokolova, and Valeria Vignudelli. Their interest in this semantics is mostly motivated by its relationship with trace semantics previously proposed in the literature. This is the subject of a forthcoming publication [8].


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Gerco van Heerdt
    • 1
  • Justin Hsu
    • 2
    Email author
  • Joël Ouaknine
    • 3
    • 4
  • Alexandra Silva
    • 1
  1. 1.Department of Computer ScienceUniversity College LondonLondonUK
  2. 2.Department of Computer SciencesUniversity of Wisconsin-MadisonMadisonUSA
  3. 3.Max Planck Institute for Software SystemsSaarbrückenGermany
  4. 4.Department of Computer ScienceOxford UniversityOxfordUK

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