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The undecidability of associativity and commutativity analysis

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Arthur CharlesworthAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 24, Issue 5

Pages 554 - 565

https://doi.org/10.1145/570886.570889

Published: 01 September 2002 Publication History

Abstract

Associativity is required for the use of general scans and reductions in parallel languages. Some systems also require functions used with scans and reductions to be commutative. We prove the undecidability of both associativity and commutativity. Thus, it is impossible in general for a compiler to check for those conditions. We also prove the stronger result that the resulting relations fail to be recursively enumerable. We prove that these results hold for the kind of function subprograms of practical interest in such a situation: function subprograms that, due to syntactical restrictions, are guaranteed to halt. Thus, our results are stronger than one can obtain from Rice's Theorem. We also obtain limitations concerning the construction of functions and limitations concerning compiler-generated run-time checks. In addition, we prove an undecidability result about programmer-constructed run-time checks.

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Cited By

Sanchez-Stern AFirst EZhou TKaufman ZBrun YRinger T(2023)Passport: Improving Automated Formal Verification Using IdentifiersACM Transactions on Programming Languages and Systems10.1145/359337445:2(1-30)Online publication date: 26-Jun-2023
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Yip EGirault ARoop PBiglari-Abhari M(2023)Synchronous Deterministic Parallel Programming for Multi-Cores with ForeCACM Transactions on Programming Languages and Systems10.1145/359159445:2(1-74)Online publication date: 26-Jun-2023
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cover image ACM Transactions on Programming Languages and Systems

ACM Transactions on Programming Languages and Systems Volume 24, Issue 5

September 2002

137 pages

ISSN:0164-0925

EISSN:1558-4593

DOI:10.1145/570886

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Copyright © 2002 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 2002

Published in TOPLAS Volume 24, Issue 5

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Cited By

Sanchez-Stern AFirst EZhou TKaufman ZBrun YRinger T(2023)Passport: Improving Automated Formal Verification Using IdentifiersACM Transactions on Programming Languages and Systems10.1145/359337445:2(1-30)Online publication date: 26-Jun-2023
https://dl.acm.org/doi/10.1145/3593374
Yip EGirault ARoop PBiglari-Abhari M(2023)Synchronous Deterministic Parallel Programming for Multi-Cores with ForeCACM Transactions on Programming Languages and Systems10.1145/359159445:2(1-74)Online publication date: 26-Jun-2023
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Basso MProkopec ARosà ABinder W(2023)Optimization-Aware Compiler-Level Event ProfilingACM Transactions on Programming Languages and Systems10.1145/359147345:2(1-50)Online publication date: 26-Jun-2023
https://dl.acm.org/doi/10.1145/3591473
Baldan PRanzato FZhang L(2022)Intensional Kleene and Rice theorems for abstract program semanticsInformation and Computation10.1016/j.ic.2022.104953289(104953)Online publication date: Nov-2022
https://doi.org/10.1016/j.ic.2022.104953
Vasiladiotis CLozano RCole MFranke BLee J(2021)Loop parallelization using dynamic commutativity analysisProceedings of the 2021 IEEE/ACM International Symposium on Code Generation and Optimization10.1109/CGO51591.2021.9370319(150-161)Online publication date: 27-Feb-2021
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Winterstein FWinterstein F(2017)Custom Multi-cache ArchitecturesSeparation Logic for High-level Synthesis10.1007/978-3-319-53222-6_5(85-115)Online publication date: 28-Feb-2017
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Winterstein FFleming KYang HBayliss SConstantinides GConstantinides GChen D(2015)MATCHUPProceedings of the 2015 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays10.1145/2684746.2689073(136-145)Online publication date: 22-Feb-2015
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Kniesburges SKoutsopoulos AScheideler C(2014)Re-ChordTheory of Computing Systems10.1007/s00224-012-9431-255:3(591-612)Online publication date: 1-Oct-2014
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