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检索条件"主题词=Recursive functions"

共 1361 条记录，以下是91-100 订阅

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Learning recursive functions from approximations 2nd

Learning recursive functions from approximations

引用

2nd European Conference on Computational Learning Theory, EuroCOLT 1995

作者： Case, John Kaufmann, Susanne Kinber, Efim Kummer, Martin Department of Computer and Information Sciences University of Delaware NewarkDE19176 United States Institut für Logik Komplexität und Deduktionssysteme Universität Karlsruhe KarlsruheD-76128 Germany

ISBN: (纸本)9783540591191

Investigated is algorithmic learning, in the limit, of correct programs for recursive functions f from both input/output examples of.f and several interesting varieties of approximate additional (algorithmic) information about f. Specifically considered, as such approximate additional information about f, are Rose's frequency computations for f and several natural generalizations from the literature, each generalization involving programs for restricted trees of recursive functions which have f as a branch. Considered as the types of trees are those with bounded variation, finite width, and finite *** the case of learning final correct programs for recursive functions, 2?X-learning, where the additional information involves frequency computations, an insightful and interestingly complex combinatorial characterization of learning power is presented as a function of the frequency parameters. Pitt has previously characterized the learning power of probabilistic machines in terms of the size of equally powerful teams of (deterministic) machines. For £X-learning (as well as for 5C-learning, where a final sequence of correct programs is learned), for the cases of providing the types of additional information considered in this paper, the optimal machine team size is determined such that the entire class of recursive functions is learnable. © Springer-Verlag Berlin Heidelberg 1995.

关键词： recursive functions

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Honest bounds for complexity classes of recursive functions 13

Honest bounds for complexity classes of recursive functions

引用

13th Annual Symposium on Switching and Automata Theory, SWAT 1972

作者： Meyer, Albert R. Moll, Robert Massachusetts Institute of Technology CambridgeMA United States

A new simplified proof of the McCreight-Meyer Honesty or Naming Theorem is given. Let t be a recursive function, and let F(t) be the set of recursive function computable within time bound t. Then it is shown that an honest recursive t′ can be found which is arbitrarily large on a dense set of arguments such that F(t) = F(t′). © 1972 IEEE.

关键词： recursive functions

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An overview of the leon verification system: Verification by translation to recursive functions

An overview of the leon verification system: Verification by...

引用

4th Workshop on Scala, SCALA 2013

作者： Blanc, Régis Kneuss, Etienne Kuncak, Viktor Suter, Philippe Switzerland

ISBN: (纸本)9781450320641

We present the Leon verification system for a subset of the Scala programming language. Along with several functional features of Scala, Leon supports imperative constructs such as mutations and loops, using a translation into recursive functional form. Both properties and programs in Leon are expressed in terms of user-defined functions. We discuss several techniques that led to an eficient semi-decision procedure for first-order constraints with recursive functions, which is the core solving engine of Leon. We describe a generational unrolling strategy for recursive templates that yields smaller satisfiable formulas and ensures completeness for counterexamples. We illustrate the current capabilities of Leon on a set of examples, such as data structure implementations;we show that Leon successfully finds bugs or proves completeness of pattern matching as well as validity of function postconditions. Copyright 2013 ACM.

关键词： recursive functions

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Automatic derivation and application of induction schemes for mutually recursive functions 1

引用

1st International Conference on Computational Logic, CL 2000

作者： Boulton, Richard J. Slind, Konrad Division of Informatics University of Edinburgh 80 South Bridge Edinburgh EH1 1HN United Kingdom University of Cambridge Computer Laboratory New Museums Site Pembroke Street Cambridge CB2 3QG United Kingdom Department of Computing Science University of Glasgow 17 Lilybank Gardens Glasgow G12 8QQ United Kingdom

ISBN: (数字)9783540449577

ISBN: (纸本)3540677976

This paper advocates and explores the use of multi-predicate induction schemes for proofs about mutually recursive functions. The interactive application of multi-predicate schemes stemming from datatype definitions is already well-established practice;this paper describes an automated proof procedure based on multi-predicate schemes. Multi-predicate schemes may be formally derived from (mutually recursive) function definitions;such schemes are often helpful in proving properties of mutually recursive functions where the recursion pattern does not follow that of the underlying datatypes. These ideas have been implemented using the HOL theorem prover and the Clam proof planner. © Springer-Verlag Berlin Heidelberg 2000.

关键词： recursive functions

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Defining and reasoning about recursive functions: A practical tool for the coq proof assistant

Defining and reasoning about recursive functions: A practica...

引用

8th International Symposium on Functional and Logic Programming, FLOPS 2006

作者： Barthe, Gilles Forest, Julien Pichardie, David Rusu, Vlad EVEREST Team INRIA Sophia-Antipolis France VERTECS Team IRISA/INRIA Rennes France

ISBN: (纸本)3540334386

We present a practical tool for defining and proving properties of recursive functions in the Coq proof assistant. The tool generates from pseudo-code the graph of the intended function as an inductive relation. Then it proves that the relation actually represents a function, which is by construction the function that we are trying to define. Then, we generate induction and inversion principles, and a fixpoint equation for proving other properties of the function. Our tool builds upon state-of-the-art techniques for defining recursive functions, and can also be used to generate executable functions from inductive descriptions of their graph. We illustrate the benefits of our tool on two case studies. © Springer-Verlag Berlin Heidelberg 2006.

关键词： recursive functions

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Automating induction over mutually recursive functions 5th

Automating induction over mutually recursive functions

引用

Proceedings of the 1996 5th International Conference on Algebraic Methodology and Software Technology, AMAST'96

作者： Kapur, D. Subramaniam, M. Computer Science Department State University of New York Albany 12222 NY United States

ISBN: (纸本)9783540614630

In order to automate proofs by induction a crucial problem that needs to be addressed is to decide on an induction scheme that leads to appropriate induction hypotheses for carrying out the proof. Boyer and Moore proposed in [5] the use of terminating function definitions for generating induction schemes. Inspired by Boyer and Moore's work, Zhang, Kapur and Krishnamoorthy introduced the cover set induction method for mechanizing induction for equational specifications in [14]. Both these approaches do not consider interaction among function definitions. Induction schemes are generated by considering function definitions in isolation, one at a time. In applications involving mutually recursive definitions, exploiting interactions among the definitions seems crucial. The cover set method implemented in the theorem prover RRL [13] as well as the methods implemented for induction in Boyer and Moore's theorem prover Nqthm based on the above approaches, do not perform well when the definitions involved are mutually recursive. Proving even very simple properties over such definitions by these methods requires some form of user intervention. We discuss how the cover set induction method implemented in RRL can be extended to automatically prove inductive properties of mutual recursive functions. An algorithm for generating cover sets from mutually recursive definitions is given. The proposed method has been implemented in the theorem prover RRL and has been extensively experimented with good results. The effectiveness of the method is illustrated using a nontrivial example of showing the equivalence of the call by value and call by name bottom-up evaluation of arithmetic expressions. A comparison of the method with those employed in Nqthm and also with an approach based on implicit induction [7, 3, 2] implemented in the theorem prover Spike is given. © Springer-Verlag Berlin Heidelberg 1996.

关键词： recursive functions

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Co-learnability and fin-identifiability of enumerable classes of total recursive functions 4th

引用

4th International Workshop on Analogical and Inductive Inference, AII 1994 and 5th International Workshop on Algorithmic Learning Theory, ALT 1994

作者： Freivalds, Rūsiņš Gobleja, Dace Karpinski, Marek Smith, Carl H. Institute of Mathematics and Computer Science University of Latvia Ralna bulv. 29 Riga Latvia Department of Computer Science University of Bonn Bonn53117 Germany International Computer Science Institute BerkeleyCA United States Department of Computer Science University of Maryland College ParkMD United States

ISBN: (纸本)9783540585206

Co-learnability is an inference process where instead of producing the final result, the strategy produces all the natural numbers but one, and the omitted number is an encoding of the correct result. It has been proved in [1] that co-learnability of Goedel numbers is equivalent to EX-identifiability. We consider co-learnability of indices in recursively enumerable (r.e.) numberings. The power of co-learnability depends on the numberings used. Every r.e. class of total recursive functions is co-learnable in some r.e. numbering. FIN-identifiable classes are co-learnable in all r.e. numberings, and classes containing a function being accumulation point are not colearnable in some r.e. numberings. Hence it was conjectured in [1] that only FIN-identifiable classes are co-learnable in all r.e. numberings. The conjecture is disproved in this paper using a sophisticated construction by ***. © 1994, Springer Verlag. All Rights Reserved.

关键词： recursive functions

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Complexity classes of partial recursive functions 71

Complexity classes of partial recursive functions

引用

3rd Annual ACM Symposium on Principles of Programming Languages, STOC 1971

作者： Robertson, Edward L. Computer Sciences Department University of Wisconsin MadisonWI53706 United States

ISBN: (纸本)9781450374644

This paper studies possible extensions of the concept of complexity class of recursive functions to partial recursive functions. Many of the wellknown results for total complexity classes are shown to have corresponding, though not exactly identical, statements for partial classes. In particular, with two important exceptions, all results on the presentation and decision problems of membership for the two most reasonable definitions of partial classes are the same as for total classes. The exceptions concern presentations of the complements and maximum difficulty for decision problems of the more restricted form of partial classes. The last section of this paper shows that it is not possible to have an "Intersection Theorem", corresponding to the Union Theorem of McCreight and Meyer, either for complexity classes or complexity index sets. © Copyright 1971 by ACM Special Interest Group for Automata and Computability Theory.

关键词： recursive functions

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Specification and verification of a formal system for structurally recursive functions

引用

Lecture Notes in Computer Science

作者： Abel, Andreas Department of Computer Science University of Munich Germany

ISBN: (纸本)3540415173

A type theoretic programming language is introduced that is based on lambda calculus with coproducts, products and inductive types, and additionally allows the definition of recursive functions in the way that is common in most functional programming languages. A formal system is presented that checks whether such a definition is structurally recursive and a soundness theorem is shown for this system. Thus all functions passing this check are ensured to terminate on all inputs. For the moment only non-mutual recursive functions are considered. © Springer-Verlag Berlin Heidelberg 2000.

关键词： recursive functions

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Learning recursive functions Refutably 12th

引用

12th Annual Conference on Algorithmic Learning Theory, ALT 2001

作者： Jain, Sanjay Kinber, Efim Wiehagen, Rolf Zeugmann, Thomas School of Computing National University of Singapore 119260 Singapore Department of Computer Science Sacred Heart University FairfieldCT06432-1000 United States Department of Computer Science University of Kaiserslautern PO Box 3049 Kaiserslautern67653 Germany Institut für Theoretische Informatik Med. Universität zu Lübeck Wallstraße 40 Lübeck23560 Germany

ISBN: (纸本)3540428755

Learning of recursive functions refutably means that for every recursive function, the learning machine has either to learn this function or to refute it, i.e., to signal that it is not able to learn it. Three modi of making precise the notion of refuting are considered. We show that the corresponding types of learning refutably are of strictly increasing power, where already the most stringent of them turns out to be of remarkable topological and algorithmical richness. All these types are closed under union, though in different strengths. Also, these types are shown to be different with respect to their intrinsic complexity;two of them do not contain function classes that are "most difficult" to learn, while the third one does. Moreover, we present characterizations for these types of learning refutably. Some of these characterizations make clear where the refuting ability of the corresponding learning machines comes from and how it can be realized, in general. For learning with anomalies refutably, we show that several results from standard learning without refutation stand refutably. Then we derive hierarchies for refutable learning. Finally, we show that stricter refutability constraints cannot be traded for more liberal learning criteria. © Springer-Verlag Berlin Heidelberg 2001.

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