A1 Refereed original research article in a scientific journal
Decision Problems for Probabilistic Finite Automata on Bounded Languages
Authors: Bell PC, Halava V, Hirvensalo M
Publisher: IOS PRESS
Publication year: 2013
Journal: Fundamenta Informaticae
Journal name in source: FUNDAMENTA INFORMATICAE
Journal acronym: FUND INFORM
Number in series: 1
Volume: 123
Issue: 1
First page : 1
Last page: 14
Number of pages: 14
ISSN: 0169-2968
DOI: https://doi.org/10.3233/FI-2013-797(external)
Abstract
For a finite set of matrices {M-1, M-2, ... , M-k} subset of Q(txt), we then consider the decidability of computing the maximal spectral radius of any matrix in the set X = {M-1(j1) M-2(j2) ... M-k(jk)vertical bar j(1), j(2), ... , j(k) >= 0}, which we call a bounded matrix language. Using an encoding of a probabilistic finite automaton shown in the paper, we prove the surprising result that determining if the maximal spectral radius of a bounded matrix language is less than or equal to one is undecidable, but determining whether it is strictly less than one is in fact decidable (which is similar to a result recently shown for quantum automata).
For a finite set of matrices {M-1, M-2, ... , M-k} subset of Q(txt), we then consider the decidability of computing the maximal spectral radius of any matrix in the set X = {M-1(j1) M-2(j2) ... M-k(jk)vertical bar j(1), j(2), ... , j(k) >= 0}, which we call a bounded matrix language. Using an encoding of a probabilistic finite automaton shown in the paper, we prove the surprising result that determining if the maximal spectral radius of a bounded matrix language is less than or equal to one is undecidable, but determining whether it is strictly less than one is in fact decidable (which is similar to a result recently shown for quantum automata).
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