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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10 Jun 2001
TL;DR: Here it is proved that there are universal time-varying distributed H-systems of degree 2, which are equivalent to any formal language of degree at least 7.
Abstract: Time-varying distributed H systems (TVDH systems shortly) of degree n are a well known model of splicing computations which has the following special feature: at different moments one uses different sets of splicing rules (the number of these sets of splicing rules is called the degree of the TVDH system). It is known that there is a universal TVDH system of degree 2. Now we prove that there is a universal TVDH system of degree 1. It is a surprising result because we did not thought that these systems are so powerful.Recently both authors proved that TVDH systems of degree 1 can generate any recursively enumerable languages. We present here the short description of the main idea of the proof that result.
9 citations
9 citations
TL;DR: The existence of a universal Σ-set as well as the existence of universal sets for higher levels of the definability hierarchy are shown.
9 citations
TL;DR: In this paper, the authors consider non-negative integers (numbers), collections of numbers (s#s) and collections of sets (classes) and denoted by small Latin letters, small Greek let ters and capital Latin letters respectively.
Abstract: 1. NOTATIONS AND TERMINOLOGY. Let us consider non-negative integers (numbers), collections of numbers (s#s) and collections of sets (classes). These entities are denoted by small Latin letters, small Greek let ters and capital Latin letters respectively. A mapping / (x 1 . . . . . x~) from certain (not necessarily all) ordered: n-tuples of numbers onto numbers is called a/unction. The words "recursively enumerable" will be abbreviated by "r.ei" The symbols + and . stand for addition and multiplication when applied to pairs0f number~, but for union and intersection when applied to pairs of sets. We write ( for inclusion. A set is immune if it is infinite, but has no infinite r.e. subset; a set is isolated, if it is finite or immune. We also use the following notations:
9 citations
TL;DR: The metatheory for Timed Modal Logic, which is the modal logic used for the analysis of timed transition systems (TTSs), is developed and it is proved that TML enjoys the Hennessy-Milner property and the set of validities are not recursively enumerable.
9 citations