On the Complexity of Szilard Languages of Regulated Grammars

Abstract

The regulated rewriting mechanism is one of the most efficient methods to augment the Chomsky hierarchy with a large variety of language classes. In this paper we investigate the derivation process in regulated rewriting grammars such as matrix grammars, programmed grammars, and random context grammars by studying their Szilard languages. We prove that Szilard languages associated with unrestricted derivations in these grammars can be recognized in logarithmic time and space by indexing alternating Turing machines. Hence, these classes of Szilard languages belong to the U E * -uniform N C 1 class [40]. In general, leftmost Szilard languages of regulated rewriting grammars can be recognized in logarithmic space and square logarithmic time. Hence, these classes of languages belong to N C 2 [40].