Polynomially Ambiguous Probabilistic Automata on Restricted Languages (Track B: Automata, Logic, Semantics, and Theory of Programming)

Author Paul C. Bell

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Paul C. Bell
  • Department of Computer Science, Byrom Street, Liverpool John Moores University, Liverpool, L3-3AF, UK


We thank the referees for their careful reading of this manuscript and their helpful improvements.

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Paul C. Bell. Polynomially Ambiguous Probabilistic Automata on Restricted Languages (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 105:1-105:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for non-strict cut-points of polynomially ambiguous PFA remains undecidable even when the input word is over a bounded language and all PFA transition matrices are commutative. In doing so, we introduce a new technique based upon the Turakainen construction of a PFA from a Weighted Finite Automata which can be used to generate PFA of lower dimensions and of subexponential ambiguity. We also study freeness/injectivity problems for polynomially ambiguous PFA and study the border of decidability and tractability for various cases.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantitative automata
  • Theory of computation → Probabilistic computation
  • Probabilistic finite automata
  • ambiguity
  • undecidability
  • bounded language
  • emptiness


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