research-article

Building Bridges between Symbolic Computation and Satisfiability Checking

Author:

Erika AbrahamAuthors Info & Claims

ISSAC '15: Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation

Pages 1 - 6

https://doi.org/10.1145/2755996.2756636

Published: 24 June 2015 Publication History

Abstract

The satisfiability problem is the problem of deciding whether a logical formula is satisfiable. For first-order arithmetic theories, in the early 20th century some novel solutions in form of decision procedures were developed in the area of mathematical logic. With the advent of powerful computer architectures, a new research line started to develop practically feasible implementations of such decision procedures. Since then, symbolic computation has grown to an extremely successful scientific area, supporting all kinds of scientific computing by efficient computer algebra systems.

Independently, around 1960 a new technology called SAT solving started its career. Restricted to propositional logic, SAT solvers showed to be very efficient when employed by formal methods for verification. It did not take long till the power of SAT solving for Boolean problems had been extended to cover also different theories. Nowadays, fast SAT-modulo-theories (SMT) solvers are available also for arithmetic problems.

Due to their different roots, symbolic computation and SMT solving tackle the satisfiability problem differently. We discuss differences and similarities in their approaches, highlight potentials of combining their strengths, and discuss the challenges that come with this task.

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Cited By

Ajani YBright C(2024)SAT and Lattice Reduction for Integer FactorizationProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669712(391-399)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1145/3666000.3669712
Bright CKotsireas IGanesh V(2022)When satisfiability solving meets symbolic computationCommunications of the ACM10.1145/350092165:7(64-72)Online publication date: 21-Jun-2022
https://dl.acm.org/doi/10.1145/3500921
Bright CKotsireas IGanesh V(2020)Applying computer algebra systems with SAT solvers to the Williamson conjectureJournal of Symbolic Computation10.1016/j.jsc.2019.07.024100:C(187-209)Online publication date: 1-Sep-2020
https://dl.acm.org/doi/10.1016/j.jsc.2019.07.024
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Index Terms

Building Bridges between Symbolic Computation and Satisfiability Checking
1. Mathematics of computing
  1. Mathematical software
2. Theory of computation
  1. Logic
  2. Models of computation
    1. Computability

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Published In

cover image ACM Conferences

ISSAC '15: Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation

June 2015

374 pages

ISBN:9781450334358

DOI:10.1145/2755996

Conference Chair:
Daniel Robertz
Plymouth University, United Kingdom
,
General Chair:
Steve Linton
University of St Andrews, United Kingdom
,
Program Chair:
Kazuhiro Yokoyama
Rikkyo University, Japan

Copyright © 2015 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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SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

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Association for Computing Machinery

New York, NY, United States

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Published: 24 June 2015

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ISSAC'15: International Symposium on Symbolic and Algebraic Computation

July 6 - 9, 2015

Bath, United Kingdom

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ISSAC '15 Paper Acceptance Rate 43 of 71 submissions, 61%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Ajani YBright C(2024)SAT and Lattice Reduction for Integer FactorizationProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669712(391-399)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1145/3666000.3669712
Bright CKotsireas IGanesh V(2022)When satisfiability solving meets symbolic computationCommunications of the ACM10.1145/350092165:7(64-72)Online publication date: 21-Jun-2022
https://dl.acm.org/doi/10.1145/3500921
Bright CKotsireas IGanesh V(2020)Applying computer algebra systems with SAT solvers to the Williamson conjectureJournal of Symbolic Computation10.1016/j.jsc.2019.07.024100:C(187-209)Online publication date: 1-Sep-2020
https://dl.acm.org/doi/10.1016/j.jsc.2019.07.024
Davenport JEngland MGriggio ASturm TTinelli C(2020)Symbolic computation and satisfiability checkingJournal of Symbolic Computation10.1016/j.jsc.2019.07.017100:C(1-10)Online publication date: 1-Sep-2020
https://dl.acm.org/doi/10.1016/j.jsc.2019.07.017
Bright CCheung KStevens BRoy DKotsireas IGanesh V(2020)A nonexistence certificate for projective planes of order ten with weight 15 codewordsApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-020-00426-y31:3-4(195-213)Online publication date: 1-Jun-2020
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Naug RKavita (2020)Assessment of Needless Code in a ProgramRising Threats in Expert Applications and Solutions10.1007/978-981-15-6014-9_2(9-18)Online publication date: 2-Oct-2020
https://doi.org/10.1007/978-981-15-6014-9_2
Seed TKing AEvans N(2020)Reducing Bit-Vector Polynomials to SAT Using Gröbner BasesTheory and Applications of Satisfiability Testing – SAT 202010.1007/978-3-030-51825-7_26(361-377)Online publication date: 26-Jun-2020
https://doi.org/10.1007/978-3-030-51825-7_26
Bright CCheung KStevens BKotsireas IGanesh V(2020)Nonexistence Certificates for Ovals in a Projective Plane of Order TenCombinatorial Algorithms10.1007/978-3-030-48966-3_8(97-111)Online publication date: 8-Jun-2020
https://dl.acm.org/doi/10.1007/978-3-030-48966-3_8
Bright CKotsireas IGanesh V(2019)SAT solvers and computer algebra systemsProceedings of the 29th Annual International Conference on Computer Science and Software Engineering10.5555/3370272.3370309(323-328)Online publication date: 4-Nov-2019
https://dl.acm.org/doi/10.5555/3370272.3370309
Bright CÐoković DKotsireas IGanesh V(2019)A SAT+CAS approach to finding good matricesProceedings of the Thirty-Third AAAI Conference on Artificial Intelligence and Thirty-First Innovative Applications of Artificial Intelligence Conference and Ninth AAAI Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v33i01.33011435(1435-1442)Online publication date: 27-Jan-2019
https://dl.acm.org/doi/10.1609/aaai.v33i01.33011435
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