It is well known that for each context-free language there exists a regular language with the same Parikh image. We investigate this result from a descriptional complexity point of view, by proving tight bounds for the size of deterministic automata accepting regular languages Parikh equivalent to some kinds of context-free languages. First, we prove that for each context-free grammar in Chomsky normal form with a fixed terminal alphabet and h variables, generating a bounded language L, there exists a deterministic automaton with at most states accepting a regular language Parikh equivalent to L. This bound, which generalizes a previous result for languages defined over a one letter alphabet, is optimal. Subsequently, we consider the case of arbitrary context-free languages defined over a two letter alphabet. Even in this case we are able to obtain a similar bound. For alphabets of at least three letters the best known upper bound is a double exponential in h. © 2012 Springer-Verlag.
CITATION STYLE
Lavado, G. J., & Pighizzini, G. (2012). Parikh’s theorem and descriptional complexity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7147 LNCS, pp. 361–372). https://doi.org/10.1007/978-3-642-27660-6_30
Mendeley helps you to discover research relevant for your work.