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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25 Jun 2007
TL;DR: This paper proves an unexpected characterization: symport/antiport P systems (and purely symport P systems with two membranes and minimal cooperation generate exactly the recursively enumerable sets of natural numbers.
Abstract: It is known that symport/antiport P systems with two membranes and minimal cooperation can generate any recursively enumerable sets of natural numbers using exactly one superfluous object in the output membrane, where the output membrane is an elementary membrane. In this paper we consider symport/antiport P systems where the output membrane is the skin membrane. In this case we prove an unexpected characterization: symport/antiport P systems (and purely symport P systems) with two membranes and minimal cooperation generate exactly the recursively enumerable sets of natural numbers.
4 citations
TL;DR: In this paper, the authors discuss the problem of determining whether any given number is in a given set A is recursive in a set B if there is an algorithm by which we can decide whether a given number x is in A, provided we are supplied with answers to all questions we choose to ask of the form Ts y in BT.
Abstract: If I have any message today for mathematicians in general, it is that consideration of difficult problems can be useful even when the problem is at present beyond solution. The problem I will discuss is unlikely to be solved in the near future, but I hope to show how the study of it leads to many more accessible problems. In order to state the problem, we need some definitions. To save words, we agree that number means natural number (nonnegative integer) and set means set of numbers. A set A is recursive if there is an algorithm for determining whether any given number is in A. A set A is recursive in a set B if there is an algorithm by which we can decide whether any given number x is in A, provided we are supplied with answers to all questions we choose to ask of the form Ts y in BT. As an example, let A ={2x : x e B}. Then B is recursive in A ; for x e B iff 2x € A. Also A is recursive in B ; for x e A iff x is even and \\x e B. (All this is independent of the choice of B.) Writing A^RB for A is recursive in B, we easily see that (1) A ^ R A ,
4 citations
TL;DR: The decidability of the existential theory of the recursively enumerable degrees in the language of Turing reducibility, Turing reduCibility of the Turing jumps, and least and greatest element is shown.
Abstract: We show the decidability of the existential theory of the recursively enumerable degrees in the language of Turing reducibility, Turing reducibility of the Turing jumps, and least and greatest element.
4 citations
4 citations
03 Sep 1984
TL;DR: This work investigates some properties of these morphic mappings and focuses on a characterization of the recursively enumerable sets, which says four homomorphisms are minimal for such representations.
Abstract: Continuing recent research of [3–9] et al. we study the composition of homomorphisms, inverse homomorphisms and twin-morphisms 〈g,h〉 and 〈g,h〉−1, where 〈g,h〉 (w) = g(w) ∩ h(w) and 〈g,h〉−1 (w) = g−1(w) ∩ h−1 (w). We investigate some properties of these morphic mappings and concentrate on a characterization of the recursively enumerable sets, which says: For every recursively enumerable set L there exist four homomorphisms such that L=f1 ° ° f 4 -1 ({$}) and L=h1 ° -1 ° h 4 -1 ({$}), and four homomorphisms are minimal for such representations.
4 citations