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Bell, PC (2022) Polynomially ambiguous probabilistic automata on restricted languages. Journal of Computer and System Sciences, 127. 53 - 65. ISSN 0022-0000
1-s2.0-S0022000022000162-main.pdf - Published Version
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Polynomially Ambiguous Probabilistic Automata.pdf - Accepted Version
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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 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 |
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Additional Information: | © 2022 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
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 |
URI: | https://eprints.keele.ac.uk/id/eprint/11105 |