Local languages and the Berry-Sethi algorithm
Theoretical Computer Science
Families of locally testable languages
Theoretical Computer Science
Automata, Languages, and Machines
Automata, Languages, and Machines
Counter-Free Automata (M.I.T. research monograph no. 65)
Counter-Free Automata (M.I.T. research monograph no. 65)
Consensual Definition of Languages by Regular Sets
Language and Automata Theory and Applications
Deterministic counter machines and parallel matching computations
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
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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.