Abstract
A recent language definition device named consensual is based on agreement between similar words. Considering, say, a regular set of words over a bipartite alphabet made by pairs of unmarked/marked letters, the match relation specifies when such words agree. Therefore a regular set (the “base”) over the bipartite alphabet specifies another language over the unmarked alphabet, called the consensual language. A word is in the consensual language if a set of corresponding matching words is in the base. From previous results, the family of consensual languages based on regular sets have an NLOGSPACE word problem, include non-semilinear languages, and are incomparable with the context-free (CF) ones; moreover the size of a consensual specification can be in a logarithmic ratio with respect to a NFA for the same language. We study the consensual languages that are produced by other language families: the Strictly Locally Testable of McNaughton and Papert and the context-free/sensitive ones. Using a recent generalization of Medvedev’s homomorphic characterization of regular languages, we prove that regular languages are exactly the consensual languages based on strictly locally testable sets, a result that hints at a novel parallel decomposition of finite automata into locally testable components. The consensual family based on context-free sets strictly includes the CF family, while the consensual and the base families collapse together if the context-sensitive languages are chosen instead of the CF.
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Crespi Reghizzi, S., San Pietro, P.L. (2012). Strict Local Testability with Consensus Equals Regularity. In: Moreira, N., Reis, R. (eds) Implementation and Application of Automata. CIAA 2012. Lecture Notes in Computer Science, vol 7381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31606-7_10
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DOI: https://doi.org/10.1007/978-3-642-31606-7_10
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