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A mechanically certified theorem about optimal concurrency of sorting networks

Authors:

Christian Lengauer and

Chua-Huang HuangAuthors Info & Claims

POPL '86: Proceedings of the 13th ACM SIGACT-SIGPLAN symposium on Principles of programming languages

January 1986

Pages 307 - 317

https://doi.org/10.1145/512644.512673

Published: 01 January 1986 Publication History

Abstract

Our concern is the mechanical certification of transformations of sequential program executions into parallel executions with equivalent semantics. The objective of such transformations is to accelerate the execution of programs. The result reported here is a mechanically certified theorem of optimality. We present a transformation which applies to every program in a particular programming language, the language of sorting networks. This transformation transforms the sequential execution of any sorting network into an execution which is as fast or faster than any other transformation which applies to every sorting network. The theorem is stated formally in a mechanized logic.

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Boyer, R. S., and Moore, J S. A Theorem Prover for Recursive Functions, a User's Manual. Computer Science Laboratory, SRI International, 1979.

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Constable, R. L., Johnson, S. D., and Eichenlaub, C. D. An Introduction to the PL/CV2 Programming Logic. Lecture Notes in Computer Science 135, Springer Verlag, 1982.

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Good, D. I. Mechanical Proofs about Computer Programs. In Mathematical Logic and Programming Languages, C. A. R. Hoare and J. S. Sheperdson, Eds., Series in Computer Science, Prentice-Hall Int., 1985, pp. 55--75.

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Huang, C.-H., and Lengauer, C. The Automated Proof of a Trace Transformation for a Bitonic Sort. TR-84-30, Department of Computer Sciences, The University of Texas at Austin, Oct., 1984.

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Knuth, D. E. The Art of Computer Programming, Vol. 3: Sorting and Searching. Addison-Wesley, 1973. Sect. 5.3.4.

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Lengauer, C., and Hehner, E. C. R. "A Methodology for Programming with Concurrency: An Informal Presentation". Science of Computer Programming 2, 1 (Oct. 1982), 1--18.

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Lengauer, C. "A Methodology for Programming with Concurrency: The Formalism". Science of Computer Programming 2, 1 (Oct. 1982), 19--52.

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Lengauer, C., and Huang, C.-H. The Static Derivation of Concurrency and Its Mechanized Certification. Proc. NSF-SERC Seminar on Concurrency, Lecture Notes in Computer Science, Springer-Verlag, 1984. To appear.

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Lengauer, C. "On the Role of Automated Theorem Proving in the Compile-Time Derivation of Concurrency". Journal of Automated Reasoning 1, 1 (1985), 75--101.

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Lengauer, C., and Huang, C.-H. A Mechanically Certified Theorem about Optimal Concurrency of Sorting Networks, and Its Proof. TR-85-23, Department of Computer Sciences, The University of Texas at Austin, 1985.

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Cited By

Boyer RMoore J(2005)A theorem prover for a computational logic10th International Conference on Automated Deduction10.1007/3-540-52885-7_75(1-15)Online publication date: 9-Jun-2005
https://doi.org/10.1007/3-540-52885-7_75
Gannett EKothari SYen H(2005)On optimal parallelization of sorting networksFoundations of Software Technology and Theoretical Computer Science10.1007/3-540-18625-5_51(195-206)Online publication date: 27-May-2005
https://doi.org/10.1007/3-540-18625-5_51
Huang CLengauer C(2005)An implemented method for incremental systolic designPARLE Parallel Architectures and Languages Europe10.1007/3-540-17943-7_127(160-177)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-17943-7_127
Show More Cited By

A mechanically certified theorem about optimal concurrency of sorting networks
1. Theory of computation
  1. Design and analysis of algorithms
    1. Data structures design and analysis
  2. Semantics and reasoning
    1. Program reasoning

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cover image ACM Conferences

POPL '86: Proceedings of the 13th ACM SIGACT-SIGPLAN symposium on Principles of programming languages

January 1986

326 pages

ISBN:9781450373470

DOI:10.1145/512644

Copyright © 1986 ACM.

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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SIGPLAN: ACM Special Interest Group on Programming Languages

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Association for Computing Machinery

New York, NY, United States

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Published: 01 January 1986

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Cited By

Boyer RMoore J(2005)A theorem prover for a computational logic10th International Conference on Automated Deduction10.1007/3-540-52885-7_75(1-15)Online publication date: 9-Jun-2005
https://doi.org/10.1007/3-540-52885-7_75
Gannett EKothari SYen H(2005)On optimal parallelization of sorting networksFoundations of Software Technology and Theoretical Computer Science10.1007/3-540-18625-5_51(195-206)Online publication date: 27-May-2005
https://doi.org/10.1007/3-540-18625-5_51
Huang CLengauer C(2005)An implemented method for incremental systolic designPARLE Parallel Architectures and Languages Europe10.1007/3-540-17943-7_127(160-177)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-17943-7_127
Gorlatch SLengauer C(1995)Parallelization of divide-and-conquer in the Bird-Meertens formalismFormal Aspects of Computing10.1007/BF012110007:6(663-682)Online publication date: 1-Nov-1995
https://dl.acm.org/doi/10.1007/BF01211000
Gorlatch SLengauer C(1994)Systematic development of an SPMD implementation schema for mutually recursive divide-and-conquer specificationsProceedings of 8th International Parallel Processing Symposium10.1109/IPPS.1994.288275(368-375)Online publication date: 1994
https://doi.org/10.1109/IPPS.1994.288275
Huang CLengauer C(1989)An incremental mechanical development of systolic solutions to the algebraic path problemActa Informatica10.1007/BF0026515027:2(97-124)Online publication date: 11-Nov-1989
https://dl.acm.org/doi/10.1007/BF00265150
Bevier WHunt WMoore JYoung W(1989)An approach to systems verificationJournal of Automated Reasoning10.1007/BF002431315:4(411-428)Online publication date: Dec-1989
https://doi.org/10.1007/BF00243131

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