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Consensual definition of languages by regular sets. (English) Zbl 1156.68452
MartĂ­n-Vide, Carlos (ed.) et al., Language and automata theory and applications. Second international conference, LATA 2008, Tarragona, Spain, March 13–19, 2008. Revised papers. Berlin: Springer (ISBN 978-3-540-88281-7/pbk). Lecture Notes in Computer Science 5196, 196-208 (2008).
Summary: A new language definition model is introduced and investigated, based on agreement or consensus between similar strings. Considering a regular set of strings over a bipartite alphabet made by pairs of unmarked/marked symbols, a match relation is introduced, in order to specify when such strings agree. Then a regular set over the bipartite alphabet can be interpreted as defining another language over the unmarked alphabet, called the consensual language. A string is in the consensual languages if a set of corresponding matching strings is in the original language. The family defined by this approach includes the regular languages and also interesting non-semilinear languages. The word problem can be solved in polynomial time, using a multi-counter machine. Closure properties of consensual languages are proved for intersection with regular sets and inverse alphabetical homomorphism.
For the entire collection see [Zbl 1148.68005].

MSC:
68Q45 Formal languages and automata
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