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Article

An efficient algorithm for solving word equations

Author:

Wojciech PlandowskiAuthors Info & Claims

STOC '06: Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing

Pages 467 - 476

https://doi.org/10.1145/1132516.1132584

Published: 21 May 2006 Publication History

Abstract

We present the first DEXPTIME algorithm which solves word equations i.e. finds a finite representation of all solutions of an equation in a free semigroup. We show how to use our approach to solve two new problems in PSPACE which deal with properties of the solution set of a word equation:

deciding finiteness of the solution set,

deciding boundness of the set of maximal exponents of periodicity of solutions.

The approach can be generalized to solve in PSPACE three problems for expressible relations, namely the emptiness of the relation, finiteness of the relation and boundness of the set of maximal exponents of periodicity of elements of the relation.

References

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G. S. Makanin. Equations in a free group. Izv. Akad. Nauk SSR Ser. Mat., 46:1199--1273, 1983. In Russian; English transl. in Math. USSR Izv. 21, 1983.]]

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W. Plandowski. Satisfiability of word equations is in nexptime. In Proceedings of the Symposium on the Theory of Computing STOC'99, pages 721--725. ACM Press, 1999.]]

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W. Plandowski. Satisfiability of word equations is in pspace. In Proceedings of the Annual Symposium on Foundations of Computer Science FOCS'99, pages 495--500. IEEE Computer Society Press, 1999.]]

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W. Plandowski. paper in preparation, 2006.]]

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W. Plandowski and W. Rytter. Application of lempel-ziv encodings to the solution of word equations. In Proceedings of the International Colloquium on Automata, Languages and Programming ICALP'98, Lecture Notes in Computer Science 1443, pages 731--742. Springer, 1998.]]

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Cited By

Abdulla PAtig MCailler JLiang CRümmer P(2024)Guiding Word Equation Solving Using Graph Neural NetworksAutomated Technology for Verification and Analysis10.1007/978-3-031-78709-6_14(279-301)Online publication date: 21-Oct-2024
https://dl.acm.org/doi/10.1007/978-3-031-78709-6_14
Wang QAppel A(2023)A Solver for Arrays with ConcatenationJournal of Automated Reasoning10.1007/s10817-022-09654-y67:1Online publication date: 7-Jan-2023
https://dl.acm.org/doi/10.1007/s10817-022-09654-y
Liu XYou WZhang ZZhang XRyu SSmaragdakis Y(2022)TensileFuzz: facilitating seed input generation in fuzzing via string constraint solvingProceedings of the 31st ACM SIGSOFT International Symposium on Software Testing and Analysis10.1145/3533767.3534403(391-403)Online publication date: 18-Jul-2022
https://dl.acm.org/doi/10.1145/3533767.3534403
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Index Terms

An efficient algorithm for solving word equations
1. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Conferences

STOC '06: Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing

May 2006

786 pages

ISBN:1595931341

DOI:10.1145/1132516

Program Chair:
Jon Kleinberg
Cornell University, Ithaca, NY

Copyright © 2006 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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Published: 21 May 2006

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word equations

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May 21 - 23, 2006

WA, Seattle, USA

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

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Cited By

Abdulla PAtig MCailler JLiang CRümmer P(2024)Guiding Word Equation Solving Using Graph Neural NetworksAutomated Technology for Verification and Analysis10.1007/978-3-031-78709-6_14(279-301)Online publication date: 21-Oct-2024
https://dl.acm.org/doi/10.1007/978-3-031-78709-6_14
Wang QAppel A(2023)A Solver for Arrays with ConcatenationJournal of Automated Reasoning10.1007/s10817-022-09654-y67:1Online publication date: 7-Jan-2023
https://dl.acm.org/doi/10.1007/s10817-022-09654-y
Liu XYou WZhang ZZhang XRyu SSmaragdakis Y(2022)TensileFuzz: facilitating seed input generation in fuzzing via string constraint solvingProceedings of the 31st ACM SIGSOFT International Symposium on Software Testing and Analysis10.1145/3533767.3534403(391-403)Online publication date: 18-Jul-2022
https://dl.acm.org/doi/10.1145/3533767.3534403
Aiswarya CMal SSaivasan P(2022)On the Satisfiability of Context-free String Constraints with Subword-OrderingProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533329(1-13)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533329
Eker S(2022)Associative unification in MaudeJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2021.100747126(100747)Online publication date: Apr-2022
https://doi.org/10.1016/j.jlamp.2021.100747
Kulczynski MLotz KNowotka DPoulsen D(2022)Solving String Theories Involving Regular Membership Predicates Using SATModel Checking Software10.1007/978-3-031-15077-7_8(134-151)Online publication date: 21-May-2022
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Day J(2022)Word Equations in the Context of String SolvingDevelopments in Language Theory10.1007/978-3-031-05578-2_2(13-32)Online publication date: 6-May-2022
https://doi.org/10.1007/978-3-031-05578-2_2
Nepeivoda A(2021)Program Specialization as a Tool for Solving Word EquationsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.341.4341(42-72)Online publication date: 6-Sep-2021
https://doi.org/10.4204/EPTCS.341.4
Amadini R(2021)A Survey on String Constraint SolvingACM Computing Surveys10.1145/348419855:1(1-38)Online publication date: 23-Nov-2021
https://dl.acm.org/doi/10.1145/3484198
Mora FBerzish MKulczynski MNowotka DGanesh V(2021)Z3str4: A Multi-armed String SolverFormal Methods10.1007/978-3-030-90870-6_21(389-406)Online publication date: 10-Nov-2021
https://doi.org/10.1007/978-3-030-90870-6_21
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