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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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Proceedings ArticleDOI
26 Jun 1995
TL;DR: The study of fixed point logics on arbitrary classes of structures shows that definability of linear order in FO+LEP although sufficient for it to capture Boolean PTIME queries, is not necessary even on the classes of rigid structures.
Abstract: We give examples of classes of rigid structures which are of unbounded rigidity but least fixed point (Partial fixed point) logic can express all Boolean PTIME (PSPACE) queries on these classes. This shows that definability of linear order in FO+LEP although sufficient for it to capture Boolean PTIME queries, is not necessary even on the classes of rigid structures. The situation however appears very different for nonzero-ary queries. Next, we turn to the study of fixed point logics on arbitrary classes of structures. We completely characterize the recursively enumerable classes of finite structures on which PFP captures all PSPACE queries of arbitrary arities. We also state in some alternative forms several natural necessary and some sufficient conditions for PFP to capture PSPACE queries on classes of finite structures. The conditions similar to the ones proposed above work for LFP and PTIME also in some special cases but to prove the same necessary conditions in general for LFP to capture PTIME seems harder and remains open.

9 citations

Journal ArticleDOI
TL;DR: It is proved that every recursively enumerable language is generated by a semi-conditional grammar of degree (2,1) with no more than seven conditional productions and eight nonterminals.

9 citations

Journal ArticleDOI
Jie Wang1
TL;DR: It is proved that for recursively enumerable sets, p-creativeness is equivalent to p-complete creativeness and Myhill's theorem still holds in the polynomial setting and these results can also be proved for NP in NEXT.

9 citations

Journal ArticleDOI
TL;DR: Much of the work on Turing degrees may be formulated in terms of the embeddability of certain first-order structures in a structure whose universe is some set of degrees and whose relations, functions, and constants are natural degree-theoretic ones.
Abstract: Since its introduction in [K1-Po], the upper semilattice of Turing degrees has been an object of fascination to practitioners of the recursion-theoretic art. Starting from relatively simple concepts and definitions, it has turned out to be a structure of enormous complexity and richness. This paper is a contribution to the ongoing study of this structure.Much of the work on Turing degrees may be formulated in terms of the embeddability of certain first-order structures in a structure whose universe is some set of degrees and whose relations, functions, and constants are natural degree-theoretic ones. Thus, for example, we know that if {P, ≤P) is a partial ordering of cardinality at most ℵ1 which is locally countable—each point has at most countably many predecessors—then there is an embeddingwhere D is the set of all Turing degrees and

9 citations

Journal ArticleDOI
TL;DR: In this article, the authors analyzed the relationship between the degrees of bases and the degree of vector spaces generated by splittings of the bases and showed that O! is the degree and dependence degree of an r.e. summand of a subspace V of Voo.
Abstract: This paper analyzes the interrelationships between the (Turing) of r.e. bases and of r.e. splittings of r.e. vector spaces together with the relationship of the degrees of bases and the degrees of the vector spaces they generate. For an r.e. subspace V of Voo , we show that O! is the degree of an r.e. basis of V iff O! is the degree of an r.e. summand of V iff O! is the degree and dependence degree of an r.e. summand of V. This result naturally leads to explore several questions regarding the degree theoretic properties of pairs of summands and the ways in which bases may arise.

9 citations

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