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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 Article
TL;DR: Inspired from biochemistry and DNA computing, several variants of controlled concatenation of strings and languages are introduced: a finite set of pairs of strings is given and two arbitrary strings are concatenated only when among their substrings the authors can find a pair in this control set.
Abstract: Inspired from biochemistry and DNA computing, we introduce several variants of controlled concatenation of strings and languages: a finite set of pairs of strings is given and two arbitrary strings are concatenated only when among their substrings (scattered substrings, of various forms) we can find a pair in this control set. Five types of non-iterated and iterated (like Kleene closure) conditional concatenations are considered. The closure properties of abstract families of languages (hence also of families in the Chomsky hierarchy) are settled. They are similar to the closure properties under usual concatenation and Kleene closure. A representation of regular languages in terms of these operations (and a coding) is also given. Then, we use the new concatenation operations as basic operations in Chomsky grammars: rewriting a nonterminal means concatenating a new string with the strings to the left and the right of that nonterminal, hence restricted concatenations can be used. Context-free grammars working in this restricted manner can generate non-context-free languages; in one case, characterizations of recursively enumerable or of context-sensitive languages are obtained, depending on using or not erasing rules. Some topics for further research are also suggested.

4 citations

Journal ArticleDOI
TL;DR: It is shown that leaving out one of the restrictions ( a ) to ( c ) yields classes of formulae whose decision problem can assume any prescribed recursively enumerable complexity in terms of many-one degrees of unsolvability.

4 citations

Journal ArticleDOI
01 Jan 1977
TL;DR: It is proved that each re language can be generated by a minimal deterministic linear contextfree based strict normal VW-grammar with at most one metanotion denoting a non-regular contextfree language.
Abstract: We show that each re language can be generated by a minimal deterministic linear contextfree based strict normal VW-grammar. We also prove that each re language can be generated by a strict normal VW-grammar with at most one metanotion denoting a non-regular contextfree language.

4 citations

Book ChapterDOI
25 Jul 2011
TL;DR: It is proved that three dynamical clusters are sufficient in general for query symbols in general, which can be interpreted as an improvement in the number of necessary clusters when compared to the case of predefined clusters.
Abstract: In this paper, we study the size complexity of nonreturning parallel communicating grammar systems First we consider the problem of determining the minimal number of components necessary to generate all recursively enumerable languages We present a construction which improves the currently known best bounds of seven (with three predefined clusters) and six (in the non-clustered case) to five, in both cases (having four clusters in the clustered variant) We also show that in the case of unary languages four components are sufficient Then, by defining systems with dynamical clusters, we investigate the minimal number of different query symbols necessary to obtain computational completeness We prove that for this purpose three dynamical clusters (which means two different query symbols) are sufficient in general, which (although the number of components is higher) can also be interpreted as an improvement in the number of necessary clusters when compared to the case of predefined clusters

4 citations

Proceedings ArticleDOI
17 Sep 2019
TL;DR: It is proved that the classical predicate logic QCL over finite domains is not recursively enumerable in the language with only three individual variables and that the set of theorems of Q CL over arbitrary domains and the set Ofsted's theorem form a recursorsively inseparable pair of recursive enumerable sets.
Abstract: We present a simple proof of Thrakhtenbrot's theorem for the classical predicate logic in the language with only three individual variables. Both forms of Thrakhtenbrot's theorem are established: we prove that the classical predicate logic QCL over finite domains is not recursively enumerable in the language with only three individual variables and that the set of theorems of QCL over arbitrary domains and the set of non-theorems of QCL over finite domains, in the language with only three individual variables, form a recursively inseparable pair of recursively enumerable sets. The techniques used here can be generalised to obtain similar results for non-classical predicate logics with further restrictions on their vocabularies.

4 citations

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