Consensual Definition of Languages by Regular Sets

Authors:
Stefano Crespi Reghizzi;Pierluigi San Pietro
Affiliations:
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milano I---20133;Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milano I---20133
Venue:
Language and Automata Theory and Applications
Year:
2008

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Abstract

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.