research-article

Monadic Decomposition

Authors:

Nikolaj Bjørner,

Lev Nachmanson,

Sergey BeregAuthors Info & Claims

Journal of the ACM (JACM), Volume 64, Issue 2

Article No.: 14, Pages 1 - 28

https://doi.org/10.1145/3040488

Published: 30 April 2017 Publication History

Abstract

Monadic predicates play a prominent role in many decidable cases, including decision procedures for symbolic automata. We are here interested in discovering whether a formula can be rewritten into a Boolean combination of monadic predicates. Our setting is quantifier-free formulas whose satisfiability is decidable, such as linear arithmetic. Here we develop a semidecision procedure for extracting a monadic decomposition of a formula when it exists.

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Cited By

Bergsträßer PGanardi MLin AZetzsche G(2024)Ramsey Quantifiers in Linear ArithmeticsProceedings of the ACM on Programming Languages10.1145/36328438:POPL(1-32)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632843
Bergsträßer PGanardi MW. Lin AZetzsche G(2022)Ramsey Quantifiers over Automatic Structures: Complexity and Applications to VerificationProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533346(1-14)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533346
Chistikov DHaase CMansutti A(2022)Quantifier elimination for counting extensions of Presburger arithmeticFoundations of Software Science and Computation Structures10.1007/978-3-030-99253-8_12(225-243)Online publication date: 29-Mar-2022
https://doi.org/10.1007/978-3-030-99253-8_12
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Index Terms

Monadic Decomposition
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Symbolic calculus algorithms
2. Theory of computation

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cover image Journal of the ACM

Journal of the ACM Volume 64, Issue 2

April 2017

277 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/3080497

Editor:
Éva Tardos
Cornell University

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Copyright © 2017 ACM.

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Publication History

Published: 30 April 2017

Accepted: 01 February 2017

Revised: 01 February 2017

Received: 01 January 2016

Published in JACM Volume 64, Issue 2

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Cited By

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https://dl.acm.org/doi/10.1145/3632843
Bergsträßer PGanardi MW. Lin AZetzsche G(2022)Ramsey Quantifiers over Automatic Structures: Complexity and Applications to VerificationProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533346(1-14)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533346
Chistikov DHaase CMansutti A(2022)Quantifier elimination for counting extensions of Presburger arithmeticFoundations of Software Science and Computation Structures10.1007/978-3-030-99253-8_12(225-243)Online publication date: 29-Mar-2022
https://doi.org/10.1007/978-3-030-99253-8_12
Markgraf OStan DLin A(2021)Learning Union of Integer Hypercubes with QueriesComputer Aided Verification10.1007/978-3-030-81688-9_12(243-265)Online publication date: 15-Jul-2021
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Hague MLin ARümmer PWu Z(2020)Monadic Decomposition in Integer Linear ArithmeticAutomated Reasoning10.1007/978-3-030-51074-9_8(122-140)Online publication date: 1-Jul-2020
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Bjørner Nde Moura LNachmanson LWintersteiger C(2019)Programming Z3Challenging the Borders of Justice in the Age of Migrations10.1007/978-3-030-17601-3_4(148-201)Online publication date: 14-Apr-2019
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Correas JMartn SSenz-Prez F(2018)Enhancing set constraint solvers with bound consistencyExpert Systems with Applications: An International Journal10.1016/j.eswa.2017.09.05692:C(485-494)Online publication date: 1-Feb-2018
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