Polynomially Ambiguous Probabilistic Automata on Restricted Languages

Bell, PC (2022) Polynomially Ambiguous Probabilistic Automata on Restricted Languages. Journal of Computer and System Sciences. ISSN 0022-0000

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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 Automata 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
Uncontrolled Keywords:	0802 Computation Theory and Mathematics, 0805 Distributed Computing, 0806 Information Systems
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QA Mathematics > QA76 Computer software
Divisions:	Computer Science and Mathematics
Publisher:	Elsevier
Date of acceptance:	9 February 2022
Date of first compliant Open Access:	24 February 2023
Date Deposited:	28 Feb 2022 12:37
Last Modified:	31 Oct 2025 09:45
DOI or ID number:	10.1016/j.jcss.2022.02.002
URI:	https://researchonline.ljmu.ac.uk/id/eprint/16436

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