Topic
Chomsky hierarchy
About: Chomsky hierarchy is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 31067 citations. The topic is also known as: Chomsky–Schützenberger hierarchy.
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TL;DR: This work corrects the earlier proof and proves that NL"S"4 is decidable in polynomial time, utilizing a technique given in Buszkowski.
4 citations
Posted Content•
TL;DR: The Borel hierarchy and the Wadge hierarchy of non-deterministic or deterministic context-free omega-languages are considered, which form the second level of the Chomsky hierarchy of languages of infinite words.
Abstract: We survey recent results on the topological complexity of context-free omega-languages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge hierarchy of non-deterministic or deterministic context-free omega-languages. We study also decision problems, the links with the notions of ambiguity and of degrees of ambiguity, and the special case of omega-powers.
4 citations
TL;DR: It is proved 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.
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 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
4 citations
4 citations
Journal Article•
TL;DR: In this article, the only remaining step in the Chomsky hierarchy is to consider those groups with a context-sensitive word problem and prove some results about these groups, and also establish some results for other context sensitive decision problems in groups.
Abstract: There already exist classifications of those groups which have regular, context-free or recursively enumerable word problem. The only remaining step in the Chomsky hierarchy is to consider those groups with a context-sensitive word problem. In this paper we consider this problem and prove some results about these groups. We also establish some results about other context-sensitive decision problems in groups.
4 citations