Bell, PC (2022) Polynomially ambiguous probabilistic automata on restricted languages. Journal of Computer and System Sciences, 127. 53 - 65. ISSN 0022-0000

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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 strict and non-strict cut-points of polynomially ambiguous commutative PFA remains undecidable, implying that the problem is undecidable when inputs are from a letter monotonic language. We show that the problem remains undecidable over a binary input alphabet when the input word is over a bounded language, in the noncommutative case. In doing so, we introduce a new technique based upon the Turakainen construction of a PFA from a Weighted Finite Automaton which can be used to generate PFA of lower dimensions and of sub-exponential ambiguity. We also study freeness/injectivity problems for polynomially ambiguous PFA and study the border of decidability and tractability for various cases.

Item Type: Article
Additional Information: © 2022 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (
Uncontrolled Keywords: Probabilistic finite automataAmbiguityUndecidabilityBounded languageFormal language theory
Subjects: T Technology > T Technology (General)
Depositing User: Symplectic
Date Deposited: 25 Jul 2022 11:15
Last Modified: 25 Jul 2022 11:15

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