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Mixed languages

By Jean Berstel, Luc Boasson and Michel Latteux

Abstract

International audienceLet T=ABC be an alphabet that is partitioned into three subalphabets. The mixing product of a word g over AB and of a word d over AC is the set of words w over T such that its projection onto AB gives g and its projection onto AC gives d. Let R be a regular language over T such that xbcy is in R if and only if xcby is in R for any two letters b in B and c in C. In other words, R is commutative over B and C. Is this property “structural” in the sense that R can then be obtained as a mixing product of a regular language over AB and of a regular language over AC? This question has a rather easy answer, but there are many cases where the answer is negative. A more interesting question is whether R can be represented as a finite union of mixed products of regular languages. For the moment, we do not have an answer to this question. However, we prove that it is decidable whether, for a given k, the language R is a union of at most k mixed products of regular languages

Topics: Formal languages, Theory of traces, Synchronized product, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Publisher: Elsevier
Year: 2005
OAI identifier: oai:HAL:hal-00150436v1
Provided by: Hal-Diderot
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