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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 reduction just mentioned requires proof, and the proof uses some form of the Brower-Konig Infinity Lemma.
Abstract: Consider the predicate of natural numbers defined by:
where R is recursive. If, as usual, the variable ƒ ranges over ω ω (the set of functions from natural numbers to natural numbers) then this is just the usual normal form for Π 1 1 sets. If, however, ƒ ranges over 2 ω (the set of functions from ω into {0, 1}) then every such predicate is recursively enumerable. 3 Thus the second type of formula is generally ignored. However, the reduction just mentioned requires proof, and the proof uses some form of the Brower-Konig Infinity Lemma.
24 citations
TL;DR: In this article, it was shown that every consistent axiomatic system S based on the functional calculus of the first order has an interpretation in the set of positive integers, where A is the conjunction of the axioms of S 2 and R 1, R 2,,, R p are the predicates that occur in A.
Abstract: Publisher Summary According to a well-known result of Lowenheim, Skolem, and Godel, every consistent axiomatic system S based on the functional calculus of the first order has an interpretation in the set of positive integers. Hence, if A is the conjunction of the axioms of S 2 and R 1 , R 2 ,…., R p are the predicates that occur in A, then there are relation R 1 , R 2 , ,…., R p (with the same number of arguments as the predicates R j ) defined in the set of positive integers which satisfy formula A in the domain of positive integers.
24 citations
24 citations
Proceedings Article•
01 Jan 2007TL;DR: A new characterization of insertion-deletion operations in linguistics and in DNA computing is contributed with a new representation of this type, as well as with representations of regular and context-free languages, mainly starting from context- free insertion systems of as small as possible complexity.
24 citations
TL;DR: The complexity of the conjugacy problem CP M for monoids given by presentations of the form T denotes a (possibly infinite) Thue system over the alphabet Σ is investigated and it is found that it can be decidable with any degree in the Grzegorczyk hierarchy or undecidable withAny recursively enumerable degree of unsolvability.
24 citations