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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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Journal ArticleDOI
TL;DR: The survey at hand picks out important studies on learning indexed families of recursive languages (including basic as well as recent research), summarizes and illustrates the corresponding results, and points out links to related fields such as grammatical inference, machine learning, and artificial intelligence in general.

68 citations

Journal ArticleDOI
TL;DR: It is proved that those data types which may be defined by conditional equation specifications and final algebra semantics are exactly the cosemicomputable data types-those data typesWhich are effectively computable, but whose inequality relations are recursively enumerable.
Abstract: We prove that those data types which may be defined by conditional equation specifications and final algebra semantics are exactly the cosemicomputable data types-those data types which are effectively computable, but whose inequality relations are recursively enumerable. And we characterize the computable data types as those data types which may be specified by conditional equation specifications using both initial algebra semantics and final algebra semantics. Numerical bounds for the number of auxiliary functions and conditional equations required are included in both theorems.

68 citations

Journal ArticleDOI
TL;DR: The main result of the present paper is the computation of the degree (in fact, isomorphism-type) of the index-set corresponding to the recursively enumerable sets of degree a: its degree is a(a); it follows from a theorem of Sacks that the degrees of such index-sets are exactly those which are > 0(3) and recursically enumerable in 0( 3).
Abstract: A class of recursively enumerable sets may be classified either as an object in itself -the range of a two-place function in the obvious way or by means of the corresponding set of indices. The latter approach is not only more precise but also, as we show below, provides an alternative method for solving certain problems on recursively enumerable sets and their degrees of unsolvability. The main result of the present paper is the computation, for every recursively enumerable degree a, of the degree (in fact, isomorphism-type) of the index-set corresponding to the recursively enumerable sets of degree a: its degree is a(. It follows from a theorem of Sacks [10] that the degrees of such index-sets are exactly those which are > 0(3) and recursively enumerable in 0(3). In particular, this proves Rogers' conjecture [9] that the index-set corresponding to Ol) is of degree 0(4); partial results on this problem have been obtained by Rogers [9] and by Lacombe (unpublished). The most interesting immediate consequence of our result is a different proof of Sacks' theorem [11] that the recursively enumerable degrees are dense. We refer the reader to Kleene [5] and Sacks [10] for our basic terminology and notation. A useful summary of many results which connect degrees with the arithmetical hierarchy is presented in [9], which is a good background to the present paper since without it the latter would not exist. For an assortment of results on classes of recursively enumerable sets the reader is referred to [2]. If e is a number and A is a set, then we define the partial function OA by setting:

66 citations

Book ChapterDOI
TL;DR: In this article, it was shown that calculable sets and calculable functions form the beginning of an infinite sequence of classes whose properties closely resemble those of projective sets, without using the notion of general recursivity.
Abstract: Publisher Summary This chapter demonstrates that calculable sets and calculable functions form the beginning of an infinite sequence of classes whose properties closely resemble those of projective sets. The theory is developed without using the notion of general recursivity. The chapter develops very extensively the theory of the new classes on the pattern of the theory of projective sets. It discusses a theorem that a recursively enumerable set whose complement is also recursively enumerable must be general recursive. The utility resulting from the analogy with projective sets is demonstrated. The chapter describes the Kuratowski–Tarski method. This method permits to evaluate the Borel class or the projective class of any set provided that its definition has been written down in logical symbols. Existence theorem is proved, and the applications to theorems of Godel and Rosser are described. Relations with the theory of general recursive function are also discussed in the chapter.

65 citations

Book ChapterDOI
TL;DR: This work considers both subsets of N obtained by counting objects in a designated membrane, and string languages obtained by following the traces of a designated object in P systems with symport/antiport generating recursively enumerable sets.
Abstract: The complexity, expressed in number of membranes and weight of rules, of P systems with symport/antiport generating recursively enumerable sets is reduced if counter automata instead of matrix grammars are simulated. We consider both subsets of N obtained by counting objects in a designated membrane, and string languages obtained by following the traces of a designated object.

65 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202220
202127
202022
201918
201823