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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01 Jan 1997
TL;DR: It is proved that any recursively enumerable language L can be homomorphically represented by twisting a linear context-free language using the combination of twist and product.
Abstract: We show that in conjunction with the usual trio operations the combination of twist and product can simulate any combination of intersection, reversal and 1/2. It is proved that any recursively enumerable language L can be homomorphically represented by twisting a linear context-free language. Indeed, the recursively enumerable sets form the least twist-closed full trio generated by dMIR:=wcw rev ¦ w e a,b *.
7 citations
01 May 1972
TL;DR: It is shown that as one increases the power of programming languages, one can obtain economies in program size by any recursive amount for even very simple functions.
Abstract: Restricted programming languages, for example primitive recursive definition schemes, are very often not nearly as succinct in describing primitive recursive functions as a general programming language [1]. We show that as one increases the power of programming languages, one can obtain economies in program size by any recursive amount for even very simple functions. This parallels a situation in the arithmetic hierarchy, where it is possible to get a recursively enumerable set whose smallest recursively enumerable index is much larger than the smallest index for the same set considered, say, as a set recursively enumerable in o'. These phenomena follow from the fact that the ability to write programs which refer to the universal functions of an enumeration enables one to decrease significantly the size of programs. The notation, when not defined is that of [4].
6 citations
TL;DR: This paper proposes some evaluation methods based on L-grammars which are fuzzy grammars for evaluation of documents in SGML-format and to the evaluation of HTML-pages in the World Wide Web and outlines how the generalization of these methods of evaluation can be applied in different contexts and for different roles.
Abstract: The large amount of information available and the difficulty on processing it has made knowledge management a promising area of research. Several topics are related to it, for example distributed and intelligent information retrieval, information filtering and information evaluation, which became crucial. In this paper, we focus our attention on the knowledge evaluation problem. With the aim of evaluating information coded in the standard non-proprietary format SGML (as also in XML), we propose some evaluation methods based on L-grammars which are fuzzy grammars. In particular we apply these methods to the evaluation of documents in SGML-format and to the evaluation of HTML-pages in the World Wide Web. L-grammars generate recursively enumerable L-languages, as it has been proved in Gerla ((1991), Information Sciences 53), and so they can be used to generate fuzzy languages based on extensions of the document type definitions (DTD) involved by SGML. Given a DTD, we extend its associated language by adding a judgement label. By selecting a particular label and by taking the start symbol of the grammar associated to the DTD, we can generate any DTD-compliant document with a fuzzy degree of membership derived from the judgement label. In this way we fit the computational model underlying the recursively enumerable L-languages to the process of collecting different evaluations of the same document. Finally, we outline how the generalization of these methods of evaluation can be applied in different contexts and for different roles, as for example for information filtering.
6 citations
01 Aug 2010
TL;DR: In this article, it was shown that the set of polynomials with integer coefficients is diophantine over R[7] and that every recursively enumerable subset of R[T] is also polynomial over R [T].
Abstract: Let R be a number field or a recursive subring of a number field and consider the polynomial ring R[T]. We show that the set of polynomials with integer coefficients is diophantine over R[7]. Applying a result by Denef, this implies that every recursively enumerable subset of R[T](k) is diophantine over R[T].
6 citations
TL;DR: It is shown that all complexity classes are non-empty and finite, and that every language-complexity class contains at least one language of each of the following types: finite, nonfinite regular, nonregular context-free, context-sensitive but not context- sensitive, recursive but notcontext-sensitive, enumerable but not recursive.
Abstract: Given a number of tape symbols, we define the state complexity of a partial-recursive function f as the minimal number of states necessary for a Turing machine that computes f. A similar definition gives us the state complexity of recursively enumerable sets and hence of abstract languages. We can show that all complexity classes are non-empty and finite. If a certain value of complexity is surpassed, then every language-complexity class contains at least one language of each of the following types: finite, nonfinite regular, nonregular context-free, context-sensitive but not context-free, recursive but not context-sensitive, enumerable but not recursive. The state complexity of a function or language is closely related to the amount of description or information needed to define the function or language.
6 citations