The Complexity of Szilard Languages of Matrix Grammars Revisited

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 mechanism in regulated rewriting grammars such as matrix grammars, by studying their Szilard languages. We focus on the complexity of Szilard languages associated with unrestricted and leftmost-like derivations in matrix grammars, with or without appearance checking. The reason is twofold. First, to relate these classes of languages to parallel complexity classes such as N C 1 and AC 1 , and, second, to improve some previous results. We prove that unrestricted Szilard languages and certain leftmost Szilard languages of context-free matrix grammars, without appearance checking, can be accepted by indexing alternating Turing machines in logarithmic time and space. Consequently, these classes are included in U E * -uniform N C 1 . Unrestricted Szilard languages of matrix grammars with appearance checking can be accepted by deterministic Turing machines in O(n log n) time and O(log n) space. Leftmost-like Szilard languages of context-free matrix grammars, with appearance checking, can be recognized by nondeterministic Turing machines by using the same time and space resources. Hence, all these classes are included in AC 1 .

On Szilard Languages of Labelled Insertion Grammars

“…The main contribution of the paper is the association of the well-known concept of Szilard languages with insertion grammars and compare the Szilard languages obtained by these grammars with the family of languages in Chomsky hierarchy. The idea of Szilard languages is well investigated in formal language theory and their closure properties, decidability aspects, complexity aspects for Chomsky grammars, matrix grammars, parallel communicating grammar systems, communicating distributive grammar systems have been investigated in [22,16,14,17,15]. Also, the idea of derivation languages (as Szilard and Control languages) has been introduced for DNA and membrane computing models in [13,21].…”