On Some Complexity Results for Even Linear Languages
Abstract
We deal with a normal form for context-free grammars, called Dyck normal form. This normal form is a syntactical restriction of the Chomsky normal form, in which the two nonterminals occurring on the right-hand side of a rule are paired nonterminals. This pairwise property, along with several other terminal rewriting conditions, makes it possible to define a homomorphism from Dyck words to words generated by a grammar in Dyck normal form. We prove that for each context-free language L, there exist an integer K and a homomorphism phi such that L=phi(D'_K), where D'_K is a subset of D_K and D_K is the one-sided Dyck language over K letters. As an application we give an alternative proof of the inclusion of the class of even linear languages in AC1.
Cite
@article{arxiv.2401.14303,
title = {On Some Complexity Results for Even Linear Languages},
author = {Liliana Cojocaru},
journal= {arXiv preprint arXiv:2401.14303},
year = {2024}
}
Comments
16 pages, no figure. arXiv admin note: substantial text overlap with arXiv:1512.09207