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.
Partially supported by PRIN 2005015419, FIRB “Applicazioni della Teoria degli Automi all’Analisi, Compilazione e Verifica di Software Critico e in Tempo Reale”, and CNR-IEIIT.
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Crespi Reghizzi, S., San Pietro, P. (2008). Consensual Definition of Languages by Regular Sets. In: Martín-Vide, C., Otto, F., Fernau, H. (eds) Language and Automata Theory and Applications. LATA 2008. Lecture Notes in Computer Science, vol 5196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88282-4_19
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DOI: https://doi.org/10.1007/978-3-540-88282-4_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88281-7
Online ISBN: 978-3-540-88282-4
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