Petri nets, commutative context-free grammars, and basic parallel processes
Fundamenta Informaticae
Two Families of Languages Related to ALGOL
Journal of the ACM (JACM)
Journal of the ACM (JACM)
A Generalization of Ogden's Lemma
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
The Complexity of Semilinear Sets
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Strong Iteration Lemmata for Regular, Linear, Context-Free, and Linear Indexed Languages
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Descriptional complexity of bounded context-free languages
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Parikh Images of Grammars: Complexity and Applications
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Parikh's theorem: A simple and direct automaton construction
Information Processing Letters
On the complexity of equational horn clauses
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
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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 $2^{h^{O(1)}}$ 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 .