The Complexity of Inductive Definability

机译：归纳可定义性的复杂性

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We study the complexity of computable and Σ_1~0 inductive definitions of sets of natural numbers. For we example, we show how to assign natural indices to monotone Σ_1~0-definitions and we use these to calculate the complexity of the set of all indices of monotone Σ_1~0-definitions which are computable. We also examine the complexity of new type of inductive definition which we call weakly finitary monotone inductive definitions. Applications are given in proof theory and in logic programming.

机译：我们研究了自然数集的可计算和Σ_1〜0归纳定义的复杂性。例如，我们展示了如何为单调Σ_1〜0定义分配自然索引，并使用这些自然索引来计算可计算的单调Σ_1〜0定义的所有索引的集合的复杂度。我们还研究了新型归纳定义的复杂性，我们将其称为弱最终单调归纳定义。在证明理论和逻辑编程中给出了应用。

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来源
《Conference on Computability in Europe(CiE 2005); 20050608-12; Amsterdam(NL)》|2005年|P.75-85|共11页
会议地点 Amsterdam(NL)
作者
Douglas Cenzer; Jeffrey B. Remmel;
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作者单位

Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, FL, USA 32611;

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原文格式 PDF
正文语种 eng
中图分类计算技术、计算机技术;
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The Complexity of Inductive Definability

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