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

Author Paul C. Bell

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Subject Classification

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

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Abstract

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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ICALP.2019.105

Author Details

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

Acknowledgements

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

References

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