Recursively enumerable language

About: Recursively enumerable language is a research topic. Over the lifetime, 1508 publications have been published within this topic receiving 32382 citations.

Effective Strategies for Enumeration Games

Abstract: We study the existence of effective winning strategies in certain infinite games, so called enumeration games. Originally, these were introduced by Lachlan (1970) in his study of the lattice of recursively enumerable sets. We argue that they provide a general and interesting framework for computable games and may also be well suited for modelling reactive systems. Our results are obtained by reductions of enumeration games to regular games. For the latter effective winning strategies exist by a classical result of Buchi and Landweber. This provides more perspicuous proofs for several of Lachlan's results as well as a key for new results. It also shows a way of how strategies for regular games can be scaled up such that they apply to much more general games.

On Context-Sensitive Grammars

Abstract: This is an overview on context-sensitive grammars. The paper contains also an appendix about Chomsky type-0 grammars (also called phrase-structure grammars). These grammars and families of languages are arising in classical language theory. Most of the topics presented in this paper are in some sense modifications of the classical notion of a rewriting system, introduced by Axel Thue at the beginning of 20th century, [44]. A rewriting system is a (finite) set of rules u → ν, where u and ν are words, indicating that an occurrence of u (as a subword) can be replaced by ν. A rewriting system only transforms words into other words, languages into other languages. After supplementing it with some mechanism for “squeezing out” a language, a rewriting system can be used as a device for defining languages. This is what Chomsky did, with linguistic goals in mind, when he introduced different types of grammars, [3, 4, 5], see also [6]. At the beginning, the classification was not very clear but by mid-60’s the four classes of the Chomsky hierarchy of grammars and languages have become pretty standard: recursively enumerable,or of type 0; context-sensitive, or of type 1; context-free, or of type 2; regular,or of type 3.

Relations between certain reducibilities

Abstract: In the paper, the concept of sQ-reducibility is introduced, and for recursively enumerable (r.e.) sets A and B, it is proved that A ≤sQ B ⇔ A ≤Q B & A ≤W B. Using this result, we give a certain characterization of contiguous degrees. It is shown that if A and B are r.e. sets such that A ≡sQ B and A