A1 Refereed original research article in a scientific journal

Decision Problems for Probabilistic Finite Automata on Bounded Languages




AuthorsBell PC, Halava V, Hirvensalo M

PublisherIOS PRESS

Publication year2013

JournalFundamenta Informaticae

Journal name in sourceFUNDAMENTA INFORMATICAE

Journal acronymFUND INFORM

Number in series1

Volume123

Issue1

First page 1

Last page14

Number of pages14

ISSN0169-2968

DOIhttps://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).



Last updated on 2024-26-11 at 22:23