Topic
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.
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TL;DR: It is shown that 1-region membrane computing systems which only use rules of the form Ca → Cv are equivalent to communication-free Petri nets, which are also equivalent to commutative context-free grammars, and that systems of the first type define precisely the semilinear sets.
47 citations
TL;DR: In this article, an explicit grouptheoretic construction based on the techniques of Britton [D] was proposed, which, if added to the Thue system constructions of [B], results in the exhibition of a finitely presented group with word problem of arbitrary recursively enumerable degree of unsolvability.
Abstract: The present paper is a sequel to [B4.2 We specify an explicit grouptheoretic construction based on techniques of Britton [D] which, if added to the Thue system constructions of [B], results in the exhibition of a finitely presented group with word problem of arbitrary recursively enumerable degree of unsolvability. One may be given the arbitrary degree as the word problem of a given Thue system. Only the results of [B] are needed, not the details, except for two definitions of notation.3 The exhibition of a finitely generated, recursively related group of arbitrary recursively enumerable degree of unsolvability (as described in [B3])2 is briefly noted. Related independent lines of development are the announcements by Cejtin [B9] (for Thue systems), and by Fridman [B13] (for finitely presented groups), as well as the detailed arguments by Clapham [Bl0] (for finitely presented groups), and by Shepherdson [B251 (for Thue systems). (See footnote 6.) Like [BI, this work is dedicated to the memory of Thoralf Skolem.
47 citations
TL;DR: Two new theorems concerning the degrees of coinfinite recursively enumerable (r.e.) sets which have no maximal supersets are presented, showing that a″ = 0″ is sufficient for an r.e. degree a to be in A, and that a′ ≥ 0′ is necessary.
Abstract: The purpose of this paper is to present two new theorems concerning the degrees of coinfinite recursively enumerable (r.e.) sets which have no maximal supersets Let the class of all such degrees be denoted by A. Martin in [2] conjectured that there was some equality or inequality involving a′ or a″ characterizing the degrees a in A. Martin himself proved ([2, Corollary 4.1]) that a′ = 0″ is sufficient for ar r.e. degree a to be in A, and Robinson [3] announced that a′ ≥ 0″ is necessary. In this paper we improve both of these theorems by a factor of the jump, i.e., we shall show that a″ = 0″ is sufficient for an r.e. degree a to be in A, and that a″ ≥ 0″ is necessary.
47 citations
TL;DR: In this paper, it was shown that given a high r.e.degree, every non-recursive d-r. degree ≦h cups toh by a low r.i.d.
Abstract: Consider the Turing degrees of differences of recursively enumerable sets (the d-r.e. degrees). We show that there is a properly d-r.e. degree (a d-r.e. degree that is not r.e.) between any two comparable r.e. degrees, and that given a high r.e. degreeh, every nonrecursive d-r.e. degree ≦h cups toh by a low d-r.e. degree.
47 citations
TL;DR: It is proved here that each recursively enumerable language can be written as the weak coding of the image by an inverse morphism of a language generated by an insertion grammar (with the maximal length of strings u, v as above equal to seven).
47 citations