Consensual languages and matching finite-state computations
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 45 (2011) no. 1, p. 77-97

An ever present, common sense idea in language modelling research is that, for a word to be a valid phrase, it should comply with multiple constraints at once. A new language definition model is studied, 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 specifying another language over the unmarked alphabet, called the consensual language. A word is in the consensual language if a set of corresponding matching strings is in the original language. The family thus defined includes the regular languages and also interesting non-semilinear ones. The word problem can be solved in NLOGSPACE, hence in P time. The emptiness problem is undecidable. Closure properties are proved for intersection with regular sets and inverse alphabetical homomorphism. Several conditions for a consensual definition to yield a regular language are presented, and it is shown that the size of a consensual specification of regular languages can be in a logarithmic ratio with respect to a DFA. The family is incomparable with context-free and tree-adjoining grammar families.

DOI : https://doi.org/10.1051/ita/2011012
Classification:  68Q45,  68Q42,  68Q19
Keywords: formal languages, finite automata, consensual languages, counter machines, polynomial time parsing, non-semilinear languages, Parikh mapping, descriptive complexity of regular languages, degree of grammaticality
@article{ITA_2011__45_1_77_0,
     author = {Crespi Reghizzi, Stefano and San Pietro, Pierluigi},
     title = {Consensual languages and matching finite-state computations},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {1},
     year = {2011},
     pages = {77-97},
     doi = {10.1051/ita/2011012},
     zbl = {1219.68112},
     mrnumber = {2776855},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2011__45_1_77_0}
}
Crespi Reghizzi, Stefano; San Pietro, Pierluigi. Consensual languages and matching finite-state computations. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 45 (2011) no. 1, pp. 77-97. doi : 10.1051/ita/2011012. http://www.numdam.org/item/ITA_2011__45_1_77_0/

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