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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
Gheorghe Paun1
TL;DR: It is proved that the P systems with the possibility of objects to cooperate characterize the recursively enumerable sets of natural numbers; moreover, systems with only two membranes suffice.

2,327 citations

Journal ArticleDOI
TL;DR: In this paper, the relation of the structure of an R set to its degree is discussed, and the infinite injury priority method is proposed to solve the problem of scaling and splitting R sets.
Abstract: TABLE OF CONTENTS Introduction Chapter I. The relation of the structure of an r.e. set to its degree. 1. Post's program and simple sets. 2. Dominating functions and quotient lattices. 3. Maximal sets and high degrees. 4. Low degrees, atomless sets, and invariant degree classes. 5. Incompleteness and completeness for noninvariant properties. Chapter II. The structure, automorphisms, and elementary theory of the r.e. sets. 6. Basic facts and splitting theorems. 7. Hh-simple sets. 8. Major subsets and r-maximal sets. 9. Automorphisms of &. 10. The elementary theory of S. Chapter III. The structure of the r.e. degrees. 11. Basic facts. 12. The finite injury priority method. 13. The infinite injury priority method. 14. The minimal pair method and lattice embeddings in R. 15. Cupping and splitting r.e. degrees. 16. Automorphisms and decidability of R.

1,932 citations

22 Apr 1987
TL;DR: In this paper, the authors discuss related theories of recursively enumerable sets, degree of un-solvability and turing degrees in particular, and generalizations of recursion theory.
Abstract: Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular. A second group of topics has to do with generalizations of recursion theory. The third topics group mentioned is subrecursive computability and subrecursive hierarchies

1,779 citations

01 Jan 1989
TL;DR: Theories of Recursive functions, Hierarchies of recursive functions, and Arithmetical sets: Recursively enumerable sets.
Abstract: Preface. Introduction. Theories of Recursive functions. Hierarchies of recursive functions. Recursively enumerable sets. Recursively enumerable degrees. Limit sets. Arithmetical sets. Arithmetical degrees. Enumeration degrees. Bibliography. Notation index. Subject index.

1,055 citations

Journal ArticleDOI
TL;DR: This paper considers classes whose elements are re-cursively enumerable sets of non-negative integers whose properties are complete recursive enumerability and complete recursiveness.
Abstract: 1. Introduction. In this paper we consider classes whose elements are re-cursively enumerable sets of non-negative integers. No discussion of recur-sively enumerable sets can avoid the use of such classes, so that it seems desirable to know some of their properties. We give our attention here to the properties of complete recursive enumerability and complete recursiveness (which may be intuitively interpreted as decidability). Perhaps our most interesting result (and the one which gives this paper its name) is the fact that no nontrivial class is completely recursive. We assume familiarity with a paper of Kleene [5](2), and with ideas which are well summarized in the first sections of a paper of Post Í7].

743 citations

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