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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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TL;DR: The central result of this paper is the small‐is‐very‐small principle for restricted sequential theories, which says roughly that whenever the given theory shows that a definable property has a small witness, then it shows that theProperty has a very small witness: i.e., a witness below a given standard number.
Abstract: The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a definable property has a small witness, i.e., a witness in a sufficiently small definable cut, then it shows that the property has a very small witness: i.e., a witness below a given standard number. Which cuts are sufficiently small will depend on the complexity of the formula defining the property. We draw various consequences from the central result. E.g., roughly speaking, (i) every restricted, recursively enumerable sequential theory has a finitely axiomatized extension that is conservative with respect to formulas of complexity ≤ n; (ii) every sequential model has, for any n, an extension that is elementary for formulas of complexity ≤ n, in which the intersection of all definable cuts is the natural numbers; (iii) we have reflection for ∑0,2 -sentences with sufficiently small witness in any consistent restricted theory U; (iv) suppose U is recursively enumerable and sequential. Suppose further that every recursively enumerable and sequential V that locally inteprets U, globally interprets U. Then, U is mutually globally interpretable with a finitely axiomatized sequential theory. The paper contains some careful groundwork developing partial satisfaction predicates in sequential theories for the complexity measure depth of quantifier alternations.
6 citations
TL;DR: It is proved that this problem of deciding the existence of codings between trace monoids is not recursively enumerable, and its decidability is shown when restricted to instances with domain monoids defined by acyclic dependence graphs.
6 citations
Book•
01 Apr 1996
6 citations
Journal Article•
TL;DR: Several characterizations of the family of the recursively enumerable lan- guages based on matrix grammars with conditions of a limited length, a reduced number of nonterminals, and a re- duced number and size of matrices are established.
Abstract: This paper discusses some conditional versions of matrix grammars. It establishes several characterizations of the family of the recursively enumerable lan- guages based on these grammars. In fact, making use of the Geffert Normal forms, the present paper demonstrates these characterizations based on matrix grammars with conditions of a limited length, a reduced number of nonterminals, and a re- duced number and size of matrices.
6 citations
TL;DR: Demonstration de quelques resultats relatifs aux paires de degres des tables de verite faibles recursivement enumerables sans infimum.
Abstract: Demonstration de quelques resultats relatifs aux paires de degres des tables de verite faibles recursivement enumerables sans infimum
6 citations