Bell, PC ORCID: https://orcid.org/0000-0003-2620-635X (2022) Polynomially ambiguous probabilistic automata on restricted languages. Journal of Computer and System Sciences, 127. 53 - 65.

[img]
Preview
Text
1-s2.0-S0022000022000162-main.pdf - Published Version

Download (454kB) | Preview
[img]
Preview
Text
Polynomially Ambiguous Probabilistic Automata.pdf - Accepted Version

Download (426kB) | Preview

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
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

Actions (login required)

View Item View Item