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The optimal fixedpoint of recursive programs

Authors:

Zohar Manna,

Adi ShamirAuthors Info & Claims

STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

Pages 194 - 206

https://doi.org/10.1145/800116.803769

Published: 05 May 1975 Publication History

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Abstract

In this paper a new fixedpoint approach towards the semantics of recursive programs is presented. The fixedpoint defined by a recursive program under this semantics contains, in some sense, the maximal amount of “interesting” information which can be extracted from the program. This optimal fixedpoint (which always uniquely exists) may be strictly more defined than the program's least fixedpoint. We consider both the theoretical and the computational aspects of the approach, as well as some techniques for proving properties of the optimal fixedpoint of a given recursive program.

References

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R. M. Burstall, "Proving Properties of Programs by Structural Induction", Computing J., Vol. 12, No. 1 (February), pp. 41-48.

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J. W. DeBakker and D. Scott, "A Theory of Programs", IBM Seminar, Vienna, Austria (August), unpublished notes.

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R. W. Floyd, "Non-deterministic Algorithms", J. ACM, Vol. 14, No. 4 (October), pp. 636-644.

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P. Hitchcock and D. Park, "Induction Rules and Termination Proofs", IRIA Conference on Automata, Languages and Programming Theory (July), pp. 183-190.

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Z. Manna, Mathematical Theory of Computation, McGraw-Hill.

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H. Rogers, Theory of Recursive Functions and Effective computability, McGraw-Hill.

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D. Scott, "Outline of a Mathematical Theory of Computation", 4th Annual Princeton Conference on Information Sciences and Systems, pp. 169-176.

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A. Shamir, "Fixedpoints of Recursive Programs", Ph.D. Thesis, Weizmann Institute, Rehovot, Israel (to appear).

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Cousot P(2023)A Personal Historical Perspective on Abstract InterpretationThe French School of Programming10.1007/978-3-031-34518-0_9(205-239)Online publication date: 11-Oct-2023
https://doi.org/10.1007/978-3-031-34518-0_9
Lehmann D(1976)Categories for fixpoint-semanticsProceedings of the 17th Annual Symposium on Foundations of Computer Science10.1109/SFCS.1976.9(122-126)Online publication date: 25-Oct-1976
https://dl.acm.org/doi/10.1109/SFCS.1976.9
Downey PSethi R(1975)Correct computation rules for recursive languagesProceedings of the 16th Annual Symposium on Foundations of Computer Science10.1109/SFCS.1975.10(48-56)Online publication date: 13-Oct-1975
https://dl.acm.org/doi/10.1109/SFCS.1975.10

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The optimal fixedpoint of recursive programs

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The optimal approach to recursive programs

The classical fixedpoint approach toward recursive programs suggests choosing the “least defined fixedpoint” as the most appropriate solution to a recursive program. A new approach is described which introduces an “optimal fixedpoint,” which, in ...
The Theoretical Aspects of the Optimal Fixedpoint

In this paper we define a new type of fixedpoint of recursive definitions and investigate some of its properties. This optimal fixedpoint (which always uniquely exists) contains, in some sense, the maximal amount of “interesting” information which can be ...
The theoretical aspects of the optimal fixedpoint

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STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

May 1975

265 pages

ISBN:9781450374194

DOI:10.1145/800116

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 05 May 1975

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STOC '75 Paper Acceptance Rate 31 of 87 submissions, 36%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cousot P(2023)A Personal Historical Perspective on Abstract InterpretationThe French School of Programming10.1007/978-3-031-34518-0_9(205-239)Online publication date: 11-Oct-2023
https://doi.org/10.1007/978-3-031-34518-0_9
Lehmann D(1976)Categories for fixpoint-semanticsProceedings of the 17th Annual Symposium on Foundations of Computer Science10.1109/SFCS.1976.9(122-126)Online publication date: 25-Oct-1976
https://dl.acm.org/doi/10.1109/SFCS.1976.9
Downey PSethi R(1975)Correct computation rules for recursive languagesProceedings of the 16th Annual Symposium on Foundations of Computer Science10.1109/SFCS.1975.10(48-56)Online publication date: 13-Oct-1975
https://dl.acm.org/doi/10.1109/SFCS.1975.10

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The Theoretical Aspects of the Optimal Fixedpoint

The theoretical aspects of the optimal fixedpoint

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The optimal approach to recursive programs

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The theoretical aspects of the optimal fixedpoint

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