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Consensual languages and matching finite-state computations

Published online by Cambridge University Press:  15 March 2011

Stefano Crespi Reghizzi
Affiliation:
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy; {crespi;sanpietro}@elet.polimi.it
Pierluigi San Pietro
Affiliation:
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy; {crespi;sanpietro}@elet.polimi.it
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, 2011

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References

Chandra, A.K., Kozen, D. and Stockmeyer, L.J., Alternation. J. ACM 28 (1981) 114133. CrossRef
Crespi Reghizzi, S. and San Pietro, P., Consensual definition of languages by regular sets, in LATA. Lecture Notes in Computer Science 5196 (2008) 196208. CrossRef
S. Crespi Reghizzi and P. San Pietro, Languages defined by consensual computations. in ICTCS09 (2009).
M. Jantzen, On the hierarchy of Petri net languages. ITA 13 (1979).
A. Joshi and Y. Schabes, Tree-adjoining grammars, in Handbook of Formal Languages, Vol. 3, G. Rozenberg and A. Salomaa, Eds. Springer, Berlin, New York (1997), 69–124.
M. Minsky, Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1976).
A. Salomaa, Theory of Automata. Pergamon Press, Oxford (1969).
Vijay-Shanker, K. and Weir, D.J., The equivalence of four extensions of context-free grammars. Math. Syst. Theor. 27 (1994) 511546. CrossRef

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