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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 demonstrated that the number of nonterminals can be decreased by one in the present characterizations if scattered context grammars start their derivations from a word rather than a single symbol.
Abstract: The syntactic complexity of scattered context grammars with respect to the number of nonterminals is investigated. First, the family of the recursively enumerable languages is characterized by some basic operations, such as quotient and coding, over the languages generated by propagating scattered context grammars with four nonterminals. Then, a new method of achieving the characterization of the family of recursively enumerable languages by scattered context grammars is given; in fact, this family is characterized by scattered context grammars with only five nonterminals and a single erasing production. Finally, it is demonstrated that the number of nonterminals can be decreased by one in the present characterizations if scattered context grammars start their derivations from a word rather than a single symbol.

11 citations

Proceedings ArticleDOI
16 Oct 1978
TL;DR: This paper is an attempt towards a systematic investigation of equality languages and fixed point languages of homomorphisms and dgsm mappings (i.e. mappings defined by deterministic generalized sequential machines with accepting states).
Abstract: A considerable part of formal language'theory deals with mappings on free monoids. A way to measure the similarity of mappings a,a on the free monoid r* generated by an alphabet E is to consider the equality language of a and a denoted by Eq(a,8) and consisting of all words x in E* such that a(x) = 6(x). To measure the similarity of a mapping with the identity mapping on the same domain one considers the fixed point language of a de~oted by Fp(a) and consisting of all words x in E such that a(x) = x (if a is a relation in r* x E* then we take Fp(a) = {x £ E* : x £ a(x)}). Thus equality languages and fixed point languages are very natural from the mathematical point of view. If we consider homomorphisms of free monoids then their equality languages represent sets of instances of the Post correspondence Problem; in this sense considering equality languages of homomorphisms is a classical topic in formal language theory (and computability theory). A revival of interest in those languages was stimulated recently by research concerning some very challenging decision problems in formal language theory; it became apparent that in several cases equality languages of homomorphisms playa vital role in (positive!) solutions of some basic equivalence problems of L systems (see e.g. (2) and [4]). This paper is an attempt towards a systematic investigation of equality languages and fixed point languages of homomorphisms and dgsm mappings (i.e. mappings defined by deterministic generalized sequential machines with accepting states). Homomorphisms and dgsm mappings are certainly among the most important mappings in formal language theory and so they form a good departure point for building up a systematic theory. Related work appears in [3] and [8]. In this extended abstract we summarize" some of the results we have obtained in this direction. It is organized as follows. Section 2 provides basic language-theoretic properties of equality languages and fixed point languages of homomorphisms. In Section 3 we present some results on the equality languages and fixed point languages of dgsm mappings but we concentrate on the subclass of dgsm mappings (that we introduce) called symmetric dgsm mappings. The theorem on fixed point languages of these mappings seems to be quite central in our theory. Then Section 4 provides an illustration of the usefulness of the classes of languages we have considered to provide various

11 citations

Book ChapterDOI
16 Jul 2015
TL;DR: A notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints – is developed, which gives a general procedure to derive the moment semantics of any such rewriting system, as a countable (and recursively enumerable) system of differential equations indexed by motif functions.
Abstract: We develop a notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the ‘no-dangling-edge’ condition inherent in DPO rewriting. Our main result is that the linear span of marked graph occurrence-counting functions – or motif functions – form an algebra which is closed under the infinitesimal generator of (the Markov chain associated with) any such rewriting system. This gives a general procedure to derive the moment semantics of any such rewriting system, as a countable (and recursively enumerable) system of differential equations indexed by motif functions. The differential system describes the time evolution of moments (of any order) of these motif functions under the rewriting system. We illustrate the semantics using the example of preferential attachment networks; a well-studied complex system, which meshes well with our notion of marked graph rewriting. We show how in this case our procedure obtains a finite description of all moments of degree counts for a fixed degree.

11 citations

Journal ArticleDOI
TL;DR: It is shown that every explanatorily learnable class can be learnt in some Friedberg numbering, however, such a result does not hold for behaviourally correct learning or finite learning.
Abstract: In this paper we consider learnability in some special numberings, such as Friedberg numberings, which contain all the recursively enumerable languages, but have simpler grammar equivalence problem compared to acceptable numberings. We show that every explanatorily learnable class can be learnt in some Friedberg numbering. However, such a result does not hold for behaviourally correct learning or finite learning. One can also show that some Friedberg numberings are so restrictive that all classes which can be explanatorily learnt in such Friedberg numberings have only finitely many infinite languages. We also study similar questions for several properties of learners such as consistency, conservativeness, prudence, iterativeness and non-U-shaped learning. Besides Friedberg numberings, we also consider the above problems for programming systems with K-recursive grammar equivalence problem.

11 citations

Book ChapterDOI
01 Jan 2013
TL;DR: A new way of associating a language with the computation of a P system, where the labels are chosen from a finite alphabet or \(\lambda .\) is considered, that associates a string that is obtained by concatenating the labels of the rules in the transition sequence corresponding to a computation.
Abstract: A new way of associating a language with the computation of a P system is considered. A label is assigned to every rule in a P system, where the labels are chosen from a finite alphabet or \(\lambda .\) We associate a string, called control word, that is obtained by concatenating the labels of the rules in the transition sequence corresponding to a computation. We study the generative capacity of such control languages comparing them with family of languages such as regular, context-free, context-sensitive and recursively enumerable languages of Chomskian hierarchy.

11 citations

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