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Decidability of cutpoint isolation for letter-monotonic probabilistic finite automata

Bell, PC and Semukhin, P (2020) Decidability of cutpoint isolation for letter-monotonic probabilistic finite automata. In: The 31st International Conference on Concurrency Theory (CONCUR 2020), 31 August 2020 - 05 September 2020, Vienna, Austria.

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We show the surprising result that the cutpoint isolation problem is decidable for probabilistic finite automata where input words are taken from a letter-bounded context-free language. A context-free language $L$ is letter-bounded when $L \subseteq a_1^*a_2^* \cdots a_k^*$ for some finite $k > 0$ where each letter is distinct. A cutpoint is isolated when it cannot be approached arbitrarily closely. The decidability of this problem is in marked contrast to the situation for the (strict) emptiness problem for PFA which is undecidable under the even more severe restrictions of PFA with polynomial ambiguity, commutative matrices and input over a letter-bounded language as well as to the injectivity problem which is undecidable for PFA over letter-bounded languages. We provide a constructive nondeterministic algorithm to solve the cutpoint isolation problem, which holds even when the PFA is exponentially ambiguous. We also show that the problem is at least NP-hard and use our decision procedure to solve several related problems.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: Probabilistic finite automata; Cutpoint isolation problem; Letter-bounded context-free languages
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics > QA76 Computer software
Divisions: Computer Science & Mathematics
Publisher: LIPIcs
Date Deposited: 29 Jul 2020 16:14
Last Modified: 13 Apr 2022 15:18
Editors: Konnov, I and Kovacs, L
URI: https://researchonline.ljmu.ac.uk/id/eprint/13401
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