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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: It is shown that for any set A there exists another set B such that the collections of r.e. languages that can be identified by machines with access to a membership oracle for B is strictly larger than the collections for r.

24 citations

Journal ArticleDOI
TL;DR: The main concern of this paper is with demonstrating, and developing a few consequences of, what might be called the “density” of hyperhypersimple sets.
Abstract: Let be the class of recursively enumerable (r.e.) sets with infinite complements. A set M ϵ is maximal if every superset of M which is in is only finitely different from M . In [1] Friedberg shows that maximal sets exist, and it is an easy consequence of this fact that every non-simple set in has a maximal superset. The natural question which arises is whether or not this is also true for every simple set (Ullian [2]). In the present paper this question is answered negatively. However, the main concern of this paper is with demonstrating, and developing a few consequences of, what might be called the “density” of hyperhypersimple sets.

24 citations

Journal ArticleDOI
TL;DR: It is shown that every recursively enumerable (RE) language can be generated by an NEP with three nodes modulo a terminal alphabet and moreover, NEPs with four nodes can generate any RE language.
Abstract: We consider the networks of evolutionary processors (NEP) introduced by J. Castellanos, C. Marti n-Vide, V. Mitrana and J. Sempere recently. We show that every recursively enumerable (RE) language can be generated by an NEP with three nodes modulo a terminal alphabet and moreover, NEPs with four nodes can generate any RE language. Thus, we improve existing universality result from five nodes down to four nodes. For mNEPs (a variant of NEPs where operations of different kinds are allowed in the same node) we obtain optimal results: each RE language can be generated by an mNEP with one node modulo a terminal alphabet, and mNEPs with two nodes can generate any RE language; this is not possible for mNEPs with one node. Some open problems are formulated.

24 citations

Journal ArticleDOI
TL;DR: It is proved that any recursively enumerable language can be determined by aGHNEP and an AHNEP with 7 nodes and it is shown that the families of GHNEPs and AHnEPs with 2 nodes are not computationally complete.

24 citations

Proceedings ArticleDOI
15 Aug 1982
TL;DR: A simple, yet comprehensive first order theory of lazy spaces relying on three axiom schemes asserting the principle of structural induction for finite objects, the existence of least upper bounds for directed sets, and the continuity of functions is developed.
Abstract: Since the publication of two influential papers on lazy evaluation in 1976 [Henderson and Morris, Friedman and Wise], the idea has gained widespread acceptance among language theoreticians—particularly among the advocates of “functional programming” [Henderson80, Backus78]. There are two basic reasons for the popularity of lazy evaluation. First, by making some of the data constructors in a functional language non-strict, it supports programs that manipulate “infinite objects” such as recursively enumerable sequences, which may make some applications easier to program. Second, by delaying evaluation of arguments until they are actually needed, it may speed up computations involving ordinary finite objects.First, there are several semantically distinct definitions of lazy evaluation that plausibly capture the intuitive notion.Second, non-trivial lazy spaces are similar in structure (under the approximation ordering) to universal domains (as defined by Scott [Scott81, Scott76]) such as the P

24 citations

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