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3rd European Conference on Computational Learning Theory, EuroCOLT 1997

作者： Smotrovs, Juris Institute of Mathematics and Computer Science University of Latvia Raina bulv. 29 RīgaLV-1459 Latvia

ISBN: (纸本)3540626859

This paper investigates closedness properties in relation with team learning of total recursive functions. One of the first problems solved for any new identification types is the following: "Does the identifiability of classes U 1 and U2 imply the identifiability of U 1∪U 2?" In this paper we are interested in a more general question: "Does the identifiability of every union of n−1 classes out of U1,...,U n imply the identifiability of U 1∪...∪U n?" If the answer is positive, we call such identification type n-closed. We show that n-closedness can be equivalently formulated in terms of team learning. After that we find for which nteam identification in the limit and team finite identification types are n-closed. In the case of team finite identification only teams in which at least half of the strategies must be successful are considered. It turns out that all these identification types, though not closed in the usual sense, are n-closed for somen>2. © Springer-Verlag Berlin Heidelberg 1997.

关键词： recursive functions

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A Macro Program for the Primitive recursive functions

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Mathematical Logic Quarterly 1991年第8期37卷 121-124页

作者： Levitz, Hilbert Nichols, Warren Smith, Robert F. Tallahassee Florida United States Durham North Carolina United States

The article discusses a macro program for the primitive recursive functions. It describes the two programming languages which is determined by programs of the language ℒ and of the other language L. L is the set of primitive recursive functions and ℒ is the set of partial recursive functions. It also presents a sketch and the details of the principal features of ℒ.

关键词： recursive functions RECURSION theory SYMBOLIC & mathematical logic PROGRAMMING languages (Electronic computers) NUMBER theory

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Probabilistic inductive inference of indices in enumerable classes of total recursive functions 2nd

Probabilistic inductive inference of indices in enumerable c...

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2nd International Workshop on Analogical and Inductive Inference, AII 1989

作者： Greitāne, Inguna Computing Center Latvian State University Riga Latvia

ISBN: (纸本)9783540517344

We consider identification of indices of functions in recursively enumerable classes of total recursive functions. The number of changes of the hypotheses is used as the complexity measure of the inductive inference machine (IIM). An efectively enumerable class U of total recursive functions is constructed such that for arbitrary E>0 there is a T-numbering of U such that:1)every deterministic IIM needs a linear number of changes of hypotheses to identify T-indices for functions in U;2)there is a probabilistic IIM which identifies T-indices for function in U with probability 1-E with a constant upper bound of changes of hypotheses. For arbitrarily slowly growing total recursive function g(n) and arbitrary T-numbering of the class U there is a probabilistic IIM such that for arbitrary p © 1989, Springer-Verlag.

关键词： recursive functions

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On the intrinsic complexity of learning recursive functions 99

On the intrinsic complexity of learning recursive functions

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Proceedings of the 1999 12th Annual Conference on Computational Learning Theory (COLT'99)

作者： Kinber, Efim Papazian, Christophe Smith, Carl Wiehagen, Rolf Sacred Heart Univ Fairfield CT United States

ISBN: (纸本)9781581131673

The intrinsic complexity of learning compares the difficulty of learning classes of objects by using some reducibility notion. For several types of learning recursive functions (learning in the limit, learning with a bounded number of mind changes, learning with anomalies), both generic complete classes are exhibited and necessary and sufficient conditions for completeness are derived. Informally, a class is complete if both its topological structure is highly complex while its algorithmic structure is surprisingly easy. Counter-intuitively, some self-describing classes turn out to be complete.

关键词： recursive functions

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Loop programs and classes of primitive recursive functions 7th

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7th Symposium on Mathematical Foundations of Computer Science, MFCS 1978

作者： Goetze, Bernhard Nehrlich, Werner Sektion Mathematik Friedrich-Schiller-Universität Jena JenaDDR - 69 Germany

ISBN: (纸本)9783540089216

A refinement of the structural complexity measure depth of nesting in loop programs leads to a new characterization of Cleave's ω2-hierarchy. This characterization allows to discover new properties (for instance Universal Function Theorem) or to reproduce already known properties of this hierarchy. A further refinement leads to a natural definition of a (ωω)-hierarchy, whose properties resemble those of Cleave's hierarchy. © 1978, Springer-Verlag.

关键词： recursive functions

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Dynamic optimization of covered tail recursive functions in applicative languages 86

Dynamic optimization of covered tail recursive functions in ...

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1986 ACM 14th Annual Conference on Computer Science, CSC 1986

作者： Felgentreu, K.-U. Lippe, W.-M. University of Munster Germany

ISBN: (纸本)0897911776

Within the last years, the interest in efficient implementations of high level interpreter-based applicative languages has increased considerably, both in the areas of software engineering and artificial intelligence. Further, a preference for static scope languages can be observed. This paper presents an optimization technique for interpreters of such languages, taking an implementation of LISP as an example. First the technique of shallow binding, which is used as a fast method of accessing variable bindings in many (dynamic scope!) LISP-systems, is adapted to static scoping. Then a dynamic optimization of simple and formal tail recursive functions is introduced. This technique is extended such that "covered tail recursire" functions are also interpreted very efficiently. functions of this kind are typical for recursive operations on list structures. Finally, it is shown that the combination of these three techniques keeps the extra expense for static scoping small. © 1986 ACM.

关键词： recursive functions

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A note on primitive recursive functions

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Proceedings of the American Mathematical Society 1955年第4期6卷 667-670页

作者： Robinson, Julia Berkeley CA United States

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Intrinsic Complexity of recursive functions on Natural Numbers with Standard Order 39

Intrinsic Complexity of Recursive Functions on Natural Numbe...

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39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022

作者： Bazhenov, Nikolay Kalociński, Dariusz Wroclawski, Michal Sobolev Institute of Mathematics Novosibirsk Russia Institute of Computer Science Polish Academy of Sciences Warsaw Poland Faculty of Philosophy University of Warsaw Poland

ISBN: (纸本)9783959772228

The intrinsic complexity of a relation on a given computable structure is captured by the notion of its degree spectrum – the set of Turing degrees of images of the relation in all computable isomorphic copies of that structure. We investigate the intrinsic complexity of unary total recursive functions on nonnegative integers with standard order. According to existing results, the possible spectra of such functions include three sets consisting of precisely: the computable degree, all c.e. degrees and all ∆2 degrees. These results, however, fall far short of the full classification. In this paper, we obtain a more complete picture by giving a few criteria for a function to have intrinsic complexity equal to one of the three candidate sets of degrees. Our investigations are based on the notion of block functions and a broader class of quasi-block functions beyond which all functions of interest have intrinsic complexity equal to the c.e. degrees. We also answer the questions raised by Wright [21] and Harrison-Trainor [10] by showing that the division between computable, c.e. and ∆2 degrees is insufficient in this context as there is a unary total recursive function whose spectrum contains all c.e. degrees but is strictly contained in the ∆2 degrees. © Nikolay Bazhenov, Dariusz Kalociński, and Michal Wroclawski.

关键词： recursive functions

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A user's friendly syntax to define recursive functions as typed λ-terms 2nd

A user's friendly syntax to define recursive functions as ty...

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2nd Annual Workshop on Types for Proofs and Programs, TYPES 1994

作者： Manoury, Pascal INRIA Domaine de Voluceau Rocquencourt Le Chesnay CedexF-78t53 France

ISBN: (纸本)9783540605799

This paper discusses the problem of translating a (recursive) function definition expressed in a ML like syntax into a typed A-term. In this paper, we recall how termination proofs can be solutions of the investigated problem. Then we recall how the method of [10] deals with the problem of searching termination proofs. Finally, we discuss the questions raised by the adaptation of our method to the Coq proof assistant. © Springer-Verlag Berlin Heidelberg 1995.

关键词： recursive functions

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The class of recursive functions

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Proceedings of the American Mathematical Society 1958年第5期9卷 690-692页

作者： Shoenfield, J.R. Duke University United States

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