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Decision Questions for Probabilistic Automata on Small Alphabets

Bell, PC and Semukhin, P (2021) Decision Questions for Probabilistic Automata on Small Alphabets. In: Leibniz International Proceedings in Informatics, LIPIcs , 202. (46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021), 23-27 August 2021, Tallinn, Estonia).

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Abstract

We study the emptiness and λ-reachability problems for unary and binary Probabilistic Finite Automata (PFA) and characterise the complexity of these problems in terms of the degree of ambiguity of the automaton and the size of its alphabet. Our main result is that emptiness and λ-reachability are solvable in EXPTIME for polynomially ambiguous unary PFA and if, in addition, the transition matrix is over {0, 1}, we show they are in NP. In contrast to the Skolem-hardness of the λ-reachability and emptiness problems for exponentially ambiguous unary PFA, we show that these problems are NP-hard even for finitely ambiguous unary PFA. For binary polynomially ambiguous PFA with commuting transition matrices, we prove NP-hardness of the λ-reachability (dimension 9), nonstrict emptiness (dimension 37) and strict emptiness (dimension 40) problems.

Item Type: Conference or Workshop Item (Paper)
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics > QA76 Computer software
Divisions: Computer Science & Mathematics
Publisher: DROPS
Date Deposited: 05 Oct 2021 09:05
Last Modified: 05 Oct 2021 09:05
DOI or Identification number: 10.4230/LIPIcs.MFCS.2021.15
URI: https://researchonline.ljmu.ac.uk/id/eprint/15599

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