A1 Refereed original research article in a scientific journal
Some decision problems concerning semilinearity and commutation
Authors: Harju T, Ibarra O, Karhumaki J, Salomaa A
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Publication year: 2002
Journal:: Journal of Computer and System Sciences
Journal name in source: JOURNAL OF COMPUTER AND SYSTEM SCIENCES
Journal acronym: J COMPUT SYST SCI
Volume: 65
Issue: 2
First page : 278
Last page: 294
Number of pages: 17
ISSN: 0022-0000
DOI: https://doi.org/10.1006/jcss.2002.1836
Abstract
Let W be a class of automata (in a precise sense to be defined) and the class obtained by augmenting each automaton in M with finitely many reversal-bounded counters. We show that if the languages defined by M are effectively semilinear, then so are the languages defined by and, hence, their emptiness problem is decidable. We give examples of how this result can be used to show the decidability of certain problems concerning the equivalence of morphisms on languages. We also prove a surprising undecidability result for commutation of languages: given a fixed two-element code K, it is undecidable whether a given context-free language L commutes with K, i.e., LK = KL. (C) 2002 Elsevier Science (USA).
Let W be a class of automata (in a precise sense to be defined) and the class obtained by augmenting each automaton in M with finitely many reversal-bounded counters. We show that if the languages defined by M are effectively semilinear, then so are the languages defined by and, hence, their emptiness problem is decidable. We give examples of how this result can be used to show the decidability of certain problems concerning the equivalence of morphisms on languages. We also prove a surprising undecidability result for commutation of languages: given a fixed two-element code K, it is undecidable whether a given context-free language L commutes with K, i.e., LK = KL. (C) 2002 Elsevier Science (USA).
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