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Interconvertbility of set constraints and context-free language reachability

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Thomas RepsAuthors Info & Claims

ACM SIGPLAN Notices, Volume 32, Issue 12

Pages 74 - 89

https://doi.org/10.1145/258994.259006

Published: 01 December 1997 Publication History

Abstract

We show the interconvertibility of context-free-language reachability problems and a class of set-constraint problems: given a context-free-language reachability problem, we show how to construct a set-constraint problem whose answer gives a solution to the reachability problem; given a set-constraint problem, we show how to construct a context-free-language reachability problem whose answer gives a solution to the set-constraint problem. The interconvertibility of these two formalisms offers an conceptual advantage akin to the advantage gained from the interconvertibility of finite-state automata and regular expressions in formal language theory, namely, a problem can be formulated in whichever formalism is most natural. It also offers some insight into the "O(n³) bottleneck" for different types of program-analysis problems, and allows results previously obtained for context-free-language reachability problems to be applied to set-constraint problems.

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Cited By

Xu PLei YSui YXue J(2024)Iterative-Epoch Online Cycle Elimination for Context-Free Language ReachabilityProceedings of the ACM on Programming Languages10.1145/36498628:OOPSLA1(1437-1462)Online publication date: 29-Apr-2024
https://doi.org/10.1145/3649862
Lei YSui YTan SZhang Q(2023)Recursive State Machine Guided Graph Folding for Context-Free Language ReachabilityProceedings of the ACM on Programming Languages10.1145/35912337:PLDI(318-342)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1145/3591233
Fähndrich MRehof JDas M(2019)Scalable context-sensitive flow analysis using instantiation constraintsACM SIGPLAN Notices10.1145/358438.34933235:5(253-263)Online publication date: 5-Jun-2019
https://dl.acm.org/doi/10.1145/358438.349332
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Index Terms

Interconvertbility of set constraints and context-free language reachability
1. Mathematics of computing
  1. Discrete mathematics
  2. Mathematical software
2. Theory of computation
  1. Formal languages and automata theory
    1. Grammars and context-free languages

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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 32, Issue 12

Dec. 1997

217 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/258994

Chairmen:
John Gallagher
Univ. of Bristol
,
Charles Consel
Univ. of Rennes/Irisa
,
Editor:
A. Michael Berman
Rowan Univ., Glassboro, NJ

Issue’s Table of Contents

PEPM '97: Proceedings of the 1997 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
December 1997
217 pages
ISBN:0897919173
DOI:10.1145/258993
Chairmen:
John Gallagher
Univ. of Bristol
,
Charles Consel
Univ. of Rennes/Irisa
,
Editor:
A. Michael Berman
Rowan Univ., Glassboro, NJ

Copyright © 1997 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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 1997

Published in SIGPLAN Volume 32, Issue 12

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Cited By

Xu PLei YSui YXue J(2024)Iterative-Epoch Online Cycle Elimination for Context-Free Language ReachabilityProceedings of the ACM on Programming Languages10.1145/36498628:OOPSLA1(1437-1462)Online publication date: 29-Apr-2024
https://doi.org/10.1145/3649862
Lei YSui YTan SZhang Q(2023)Recursive State Machine Guided Graph Folding for Context-Free Language ReachabilityProceedings of the ACM on Programming Languages10.1145/35912337:PLDI(318-342)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1145/3591233
Fähndrich MRehof JDas M(2019)Scalable context-sensitive flow analysis using instantiation constraintsACM SIGPLAN Notices10.1145/358438.34933235:5(253-263)Online publication date: 5-Jun-2019
https://dl.acm.org/doi/10.1145/358438.349332
Steinhauser AGauthier FMurray TStefan D(2016)JSPCheckerProceedings of the 2016 ACM Workshop on Programming Languages and Analysis for Security10.1145/2993600.2993606(57-68)Online publication date: 24-Oct-2016
https://dl.acm.org/doi/10.1145/2993600.2993606
FÄHNDRICH MREHOF J(2008)Type-based flow analysis and context-free language reachabilityMathematical Structures in Computer Science10.1017/S096012950800696818:05(823)Online publication date: 6-Oct-2008
https://doi.org/10.1017/S0960129508006968
Zhang YNielson F(2008)A Scalable Inclusion Constraint Solver Using UnificationLogic-Based Program Synthesis and Transformation10.1007/978-3-540-78769-3_9(121-137)Online publication date: 28-Nov-2008
https://dl.acm.org/doi/10.1007/978-3-540-78769-3_9
Fecht CSeidl H(2006)Propagating differences: An efficient new fixpoint algorithm for distributive constraint systemsProgramming Languages and Systems10.1007/BFb0053565(90-104)Online publication date: 23-May-2006
https://doi.org/10.1007/BFb0053565
Fähndrich MRehof JDas MLam M(2000)Scalable context-sensitive flow analysis using instantiation constraintsProceedings of the ACM SIGPLAN 2000 conference on Programming language design and implementation10.1145/349299.349332(253-263)Online publication date: 1-Aug-2000
https://dl.acm.org/doi/10.1145/349299.349332
Reps T(1998)Program analysis via graph reachabilityInformation and Software Technology10.1016/S0950-5849(98)00093-740:11-12(701-726)Online publication date: Dec-1998
https://doi.org/10.1016/S0950-5849(98)00093-7
Ren JSui YCheng XFeng YZhao J(2024)Dynamic Transitive Closure-based Static Analysis through the Lens of Quantum SearchACM Transactions on Software Engineering and Methodology10.1145/364438933:5(1-29)Online publication date: 4-Jun-2024
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