Morphic characterizations of languages in Chomsky hierarchy with insertion and locality

Kaoru Fujioka
2011 Information and Computation  
This paper concerns new characterizations of regular, context-free, and recursively enumerable languages, using insertion systems with lower complexity. This is achieved by using both strictly locally testable languages and morphisms. The representation is in a similar way to the Chomsky-Schützenberger representation of context-free languages. Specifically, each recursively enumerable language L can be represented in the form L = h(L(γ ) ∩ R), where γ is an insertion system of weight (3, 3) , R
more » ... is a strictly 2-testable language, and h is a projection. A similar representation can be obtained for context-free languages, using insertion systems of weight (2, 0) and strictly 2-testable languages, as well as for regular languages, using insertion systems of weight (1, 0) and strictly 2-testable languages.
doi:10.1016/j.ic.2010.11.011 fatcat:d46gkl4rwzg45due2d4rkqkqru