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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TL;DR: Goncharov and Badaev as mentioned in this paper showed that there are infinite families whose Rogers semilattices contain ideals without minimal elements, and they proved that independently of a family chosen, the class of semi-attices that are principal ideals of that family is rather wide: it includes both a factor lattice of recursively enumerable sets modulo finite sets and a family of initial segments in the semiilattice of m-degrees generated by immune sets.
Abstract: S. Goncharov and S. Badaev showed that for \(n \geqslant 2\), there exist infinite families whose Rogers semilattices contain ideals without minimal elements. In this connection, the question was posed as to whether there are examples of families that lack this property. We answer this question in the negative. It is proved that independently of a family chosen, the class of semilattices that are principal ideals of the Rogers semilattice of that family is rather wide: it includes both a factor lattice of the lattice of recursively enumerable sets modulo finite sets and a family of initial segments in the semilattice of \(m\)-degrees generated by immune sets.
8 citations
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TL;DR: The question whether easiness implies simple easiness constitutes Problem 19 in the TLCA list of open problems is negatively answered, providing a non-empty co-r.e. (complement of a recursively enumerable) set of easy, but not simple easy, λ -terms.
Abstract: A closed λ -term M is easy if, for any
other closed term N , the lambda theory generated by
M = N is consistent. Recently, it has been introduced
a general technique to prove the easiness of λ -terms through the
semantical notion of simple easiness. Simple easiness implies easiness and allows to prove
consistency results via construction of suitable filter models of
λ -calculus living in the category of complete partial orderings: given
a simple easy term M and an arbitrary closed term N , it
is possible to build (in a canonical way) a non-trivial filter model which equates the
interpretation of M and N . The question whether easiness
implies simple easiness constitutes Problem 19 in the TLCA list of open problems. In this
paper we negatively answer the question providing a non-empty co-r.e. (complement of a
recursively enumerable) set of easy, but not simple easy, λ -terms.
8 citations
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TL;DR: An axiomatic theory of “generalized Routley-Meyer (GRM) logics” is developed which shows that all GRM logics are subclassical, have recursively enumerable consequence relations, satisfy the compactness theorem, and satisfy the standard structural rules and conjunction and disjunction introduction/elimination rules.
Abstract: We develop an axiomatic theory of “generalized Routley-Meyer (GRM) logics.” These are first-order logics which are can be characterized by model theories in a certain generalization of Routley-Meyer semantics. We show that all GRM logics are subclassical, have recursively enumerable consequence relations, satisfy the compactness theorem, and satisfy the standard structural rules and conjunction and disjunction introduction/elimination rules. We also show that the GRM logics include classical logic, intuitionistic logic, LP/K3/FDE, and the relevant logics.
8 citations
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13 Dec 1984TL;DR: A terminal weighted grammar is defined where the terminal generated at any step of a derivation is defined as a function of time and it is seen that terminal weighted regular grammars generate exactly the class of recursively enumerable sets.
Abstract: Motivated by the idea of describing parquet deformations using grammars, we define in this paper a terminal weighted grammar where the terminal generated at any step of a derivation is defined as a function of time. It is seen that terminal weighted regular grammars generate exactly the class of recursively enumerable sets. Terminal weighted matrix grammars are used to describe parquet deformations. The hierarchy of families generated by putting various restrictions on the functions is studied.
8 citations