scispace - formally typeset
Search or ask a question
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.


Papers
More filters
01 Jan 2008
TL;DR: A specific, natural embedding of RT is defined into a slightly larger degree structure, Pw, which is much better behaved, and some recent and new research results are presented.
Abstract: Recall that RT is the upper semilattice of recursively enumerable Turing degrees. We consider two fundamental, classical, unresolved issues concerning RT . The first issue is to find a specific, natural, recursively enumerable Turing degree a ∈ RT which is > 0 and 0 and < 0′. In order to address these issues, we embedRT into a slightly larger degree structure, Pw, which is much better behaved. Namely, Pw is the lattice of weak degrees of mass problems associated with nonempty Π01 subsets of 2 ω . We define a specific, natural embedding of RT into Pw, and we present some recent and new research results. Preface This paper is based on my talks in Evanston, Illinois, October 24, 2004, and in Singapore, August 8, 2005. The Evanston talk was part of a regional meeting of the American Mathematical Society, held at Northwestern University, October 23–24, 2004. The Singapore talk was part of a workshop entitled Computational Prospects of Infinity, held at the Institute for Mathematical Sciences, National University of Singapore, June 20 through August 15, 2005. The research reported in this paper was partially supported by my NSF research grant DMS-0070718, 2000–2004. Preparation of this paper was partially supported by my NSF research grant DMS-0600823, 2006–2009. These grants are from the National Science Foundation of the U.S.A. Motivation Recall that DT is the upper semilattice consisting of all Turing degrees. Recall also that RT is the countable sub-semilattice of DT consisting of the recur-

10 citations

Book ChapterDOI
01 Jul 2013
TL;DR: This work considers a way to associate a language with the computations of a tissue P system, and assigns a label to every rule, where the labels are chosen from an alphabet or the label can be λ.
Abstract: We consider a way to associate a language with the computations of a tissue P system. We assign a label to every rule, where the labels are chosen from an alphabet or the label can be λ. The rules used in a transition should have either the empty label or the same label from the chosen alphabet. In this way, a string is associated with each halting computation, called the control word of the computation. The set of all control words associated with computations in a tP system form the control language of the system. We study the family of control languages of tP systems in comparison with the families of finite, regular, context-free, context-sensitive, and recursively enumerable languages.

10 citations

01 Jan 2001
TL;DR: In this article, it was shown that the equational theory of RPA! is non-recursively enumerable in the generalized sense. But this result does not imply that RPA!, as a class of representable polyadic algebras, is also non-computable.
Abstract: In [3] Daigneault and Monk proved that the class of (! dimensional) representable polyadic algebras (RPA! for short) is axiomatizable by finitely many equationschemas. However, this result does not imply that the equational theory of RPA! would be recursively enumerable; one simple reason is that the language of RPA! contains a continuum of operation symbols. Here we prove the following. Roughly, for any reasonable generalization of computability to uncountable languages, the equational theory of RPA! remains non-recursively enumerable, or non-computable, in the generalized sense. This result has some implications on the non-computational character of Keisler’s completeness theorem for his “infinitary logic” in Keisler [6] as well.

10 citations

Network Information
Related Topics (5)
Decidability
9.9K papers, 205.1K citations
91% related
Multimodal logic
6.1K papers, 178.8K citations
86% related
Type (model theory)
38.9K papers, 670.5K citations
86% related
Dynamic logic (modal logic)
6.6K papers, 210.3K citations
86% related
Mathematical proof
13.8K papers, 374.4K citations
84% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202220
202127
202022
201918
201823