Non-deterministic Weighted Automata on Random Words

Authors Jakub Michaliszyn, Jan Otop

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Jakub Michaliszyn
  • University of Wrocław
Jan Otop
  • University of Wrocław

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Jakub Michaliszyn and Jan Otop. Non-deterministic Weighted Automata on Random Words. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We present the first study of non-deterministic weighted automata under probabilistic semantics. In this semantics words are random events, generated by a Markov chain, and functions computed by weighted automata are random variables. We consider the probabilistic questions of computing the expected value and the cumulative distribution for such random variables. The exact answers to the probabilistic questions for non-deterministic automata can be irrational and are uncomputable in general. To overcome this limitation, we propose an approximation algorithm for the probabilistic questions, which works in exponential time in the automaton and polynomial time in the Markov chain. We apply this result to show that non-deterministic automata can be effectively determinised with respect to the standard deviation metric.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Quantitative automata
  • Mathematics of computing → Markov networks
  • quantitative verification
  • weighted automata
  • expected value


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