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. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Reghizzi, S. C., & San Pietro, P. (2008). Consensual definition of languages by regular sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5196 LNCS, pp. 196–208). https://doi.org/10.1007/978-3-540-88282-4_19
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