On szilard languages of pure context-free grammars
Journal of Information Processing and Cybernetics
Formal languages
The complexity of Boolean functions
The complexity of Boolean functions
Grammars with controlled derivations
Handbook of formal languages, vol. 2
Journal of the ACM (JACM)
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Regulated Rewriting in Formal Language Theory
Regulated Rewriting in Formal Language Theory
Renaming and Erasing in Szilard Languages
Proceedings of the Fourth Colloquium on Automata, Languages and Programming
Classes of Szilard Languages in NC^1
SYNASC '09 Proceedings of the 2009 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
On the Complexity of Szilard Languages of Matrix Grammars
SYNASC '11 Proceedings of the 2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Structural Complexity II
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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 NC1 and AC1, 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 UE*-uniform NC1. Unrestricted Szilard languages of matrix grammars with appearance checking can be accepted by deterministic Turing machines in On log n time and Olog 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 AC1.