research-article

Free access

Satisfiability modulo theories: introduction and applications

Authors:

Leonardo De Moura,

Nikolaj BjørnerAuthors Info & Claims

Communications of the ACM, Volume 54, Issue 9

Pages 69 - 77

https://doi.org/10.1145/1995376.1995394

Published: 01 September 2011 Publication History

All formats PDF

Abstract

Checking the satisfiability of logical formulas, SMT solvers scale orders of magnitude beyond custom ad hoc solvers.

References

[1]

Audemard, G., Bertoli, P., Cimatti, A., Kornilowicz, A., and Sebastiani, R. A SAT -based approach for solving formulas over Boolean and linear mathematical propositions. In Proceedings of the Conference on Automated Deduction, Vol. 2392 of LNCS (Copenhagen, July 27--30). Springer-Verlag, Berlin, 2002.

Digital Library

[2]

Ball, T. and Rajamani, S.K. The SLAM project: Debugging system software via static analysis. (Symposium on Principles of Programming Languages). SIGPLAN Notices 37, 1 (Jan. 16--18, 2002), 1--3.

Digital Library

[3]

Barnett, M., Leino, K.R.M., and Schulte, W. The Spec# programming system: An overview. In Proceedings of the International Workshop on Construction and Analysis of Safe, Secure and Interoperable Smart Devices, LNCS 3362 (Marseille, Mar. 10--13). Springer-Verlag, Berlin, 2005, 49--69.

Digital Library

[4]

Barrett, C., de Moura, L., and Stump, A. Design and results of the first Satisfiability Modulo Theories Competition. Journal of Automated Reasoning 35, 4 (Nov. 2005), 372--390.

Digital Library

[5]

Barrett, C., Dill, D., and Stump, A. Checking satisfiability of first-order formulas by incremental translation to SAT. In Proceedings of the International Conference on Computer Aided Verification (Copenhagen, July, 27--31). Springer-Verlag, Berlin 2002, 236--249.

Digital Library

[6]

Barrett, C., Sebastiani, R., Seshia, S.A., and Tinelli, C. Satisfiability Modulo Theories, Vol. 185 of Frontiers in Artificial Intelligence and Applications, Chapter 26. IOS Press, Feb. 2009, 825--885.

[7]

Barrett, C. and Tinelli, C. CVC3. In Proceedings of the 19th International Conference on Computer Aided Verification, Vol. 4590 of LNCS, W. Damm and H. Hermanns, Eds. (Berlin, July 3--7). Springer-Verlag, Berlin, 2007, 298--302.

Digital Library

[8]

Bofill, M., Nieuwenhuis, R., Oliveras, A., Rodríguez Carbonell, E., and Rubio, A. The Barcelogic SMT Solver. In Proceedings of the 20th International Conference on Computer Aided Verification, Vol. 5123 of LNCS, A. Gupta and S. Malik, Eds. (Princeton, July 7--14). Springer-Verlag, Berlin, 2008, 294--298.

Digital Library

[9]

Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T.A., Ranise, S., van Rossum, P., and Sebastiani, R. Efficient satisfiability modulo theories via delayed theory combination. In Proceedings of the International Conference on Computer Aided Verification, Vol. 3576 of LNCS, K. Etessami and S. K. Rajamani, Eds. (Edinburgh, July 6--12). Springer-Verlag, Berlin, 2005, 335--349.

Digital Library

[10]

Bruttomesso, R., Cimatti, A., Franzén, A., Griggio, A., and Sebastiani, R. The MathSAT 4 SMT Solver. In Proceedings of the 18th International Conference on Computer Aided Verification, Vol. 5123 of LNCS. Springer-Verlag, Berlin, 2008.

Digital Library

[11]

Cohen, E., Dahlweid, M., Hillebrand, M., Leinenbach, D., Moskal, M., Santen, T., Schulte, W., and Tobies, S. VCC: A practical system for verifying concurrent C. In Proceedings of the International Conference on Theorem Proving in Higher Order Logics (Munich, Aug. 17--20). Springer-Verlag. Berlin, 2009, 23--42.

Digital Library

[12]

Cook, S.A. The complexity of theorem-proving procedures. In Proceedings of the Third Annual ACM Symposium on Theory of Computing (May 3--5). ACM Press, New York, 1971, 151--158.

Digital Library

[13]

Davis, M., Logemann, G., and Loveland, D. A machine program for theorem proving. Commun. ACM 5, 2 (July 1962), 394--397.

Digital Library

[14]

de Moura, L. and Bjørner, N. Z3: An efficient SMT solver. In Proceedings of the International Conference on tools and algorithms for the Construction and Analysis of Systems, Vol. 4963 of LNCS, C.R. Ramakrishnan and J. Rehof, Eds. (Budapest, Mar. 29- Apr. 6). Springer-Verlag, Berlin, 2008, 337--340.

Digital Library

[15]

de Moura, L. and Rueß, H. Lemmas on demand for satisfiability solvers. In Proceedings of the International Conference on Theory and Applications of Satisfiability Testing (Cincinnati, May 6--9, 2002).

[16]

Detlefs, D., Nelson, G., and Saxe, J.B. Simplify: A theorem prover for program checking. Journal of the ACM 52, 3 (May 2005), 365--473.

Digital Library

[17]

Downey, P.J., Sethi, R., and Tarjan, R.E. Variations on the common subexpression problem. Journal of the ACM 27, 4 (Oct. 1980), 758--771.

Digital Library

[18]

Dutertre, B. and de Moura, L. A fast linear-arithmetic solver for DPLL(T). In Proceedings of the 16th International Conference on Computer Aided Verification, Vol. 4144 of LNCS (Seattle, Aug. 17--20). Springer-Verlag, Berlin, 2006, 81--94.

Digital Library

[19]

Filliâtre, J.-C. Why: A Multi-Language Multi-Prover Verification Tool. Technical Report 1366, Université Paris Sud, 2003.

[20]

Flanagan, C., Joshi, R., Ou, X., and Saxe, J.B. Theorem proving using lazy proof explication. In Proceedings of the 15th International Conference on Computer Aided Verification (Boulder, CO, July 8--12). Springer-Verlag, Berlin, 2003, 355--367.

[21]

Flanagan, C., Leino, K.R.M., Lillibridge, M., Nelson, G., Saxe, J.B., and Stata, R. Extended static checking for Java. In Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (Berlin, June 17--19). ACM Press, New York, 2002, 234--245.

Digital Library

[22]

Ghilardi, S., Nicolini, E., and Zucchelli, D. A comprehensive framework for combined decision procedures. In Proceedings of the Fifth International Workshop on Frontiers of Combining Systems, Vol. 3717 of LNCS, B. Gramlich, Ed. (Vienna, Sept. 19--21). Springer-Verlag, Berlin, 2005, 1--30.

Digital Library

[23]

Godefroid, P., de Halleux, J., Nori, A.V., Rajamani, S.K., Schulte, W., Tillmann, N., and Levin, M.Y. Automating software testing using program analysis. IEEE Software 25, 5 (Sept./Oct. 2008), 30--37.

Digital Library

[24]

Grieskamp, W., Kicillof, N., MacDonald, D., Nandan, A., Stobie, K., and Wurden, F.L. Model-based quality assurance of Windows protocol documentation. In Proceedings of the First International Conference on Software Testing, Verification, and Validation (Lillehammer, Norway, Apr. 9--11). IEEE Computer Society Press, 2008, 502--506.

Digital Library

[25]

Henzinger, T.A., Jhala, R., Majumdar, R., and Sutre, G. Software verification with blast. In Proceedings of the 10th International SPIN Workshop, Vol. 2648 of LNCS, T. Ball and S. R. Rajamani, Eds. (Portland, May 9--10). Springer-Verlag, Berlin, 2003, 235--239.

Digital Library

[26]

Kaufmann, M., Manolios, P., and Moore, J.S. Computer-Aided Reasoning: An Approach. Kluwer Academic, June 2000.

Digital Library

[27]

Malik, S. and Zhang, L. Boolean satisfiability from theoretical hardness to practical success. Commun. ACM 52, 8 (Aug. 2009), 76--82.

Digital Library

[28]

McCarthy, J. Towards a mathematical science of computation. In Congress of the International Federation for Information Processing, 1962, 21--28.

[29]

Nelson, G. and Oppen, D.C. Simplification by cooperating decision procedures. ACM Transactions on Programming Languages and Systems 1, 2 (Oct. 1979), 245--257.

Digital Library

[30]

Nieuwenhuis, R., Oliveras, A., and Tinelli, C. Solving SAT and SAT modulo theories: From an abstract Davis--Putnam--Logemann--Loveland procedure to DPLL(T). Journal of the ACM 53, 6 (Nov. 2006), 937--977.

Digital Library

[31]

Oppen, D.C. Complexity, convexity and combinations of theories. Theoretical Computer Science 12, 3 (1980), 291--302.

[32]

Owre, S., Rushby, J.M., and Shankar, N. PVS: A prototype verification system. In Proceedings of the 11th International Conference on Automated Deduction (Saratoga, NY, June 15--18). Springer-Verlag, Berlin, 1992, 748--752.

Digital Library

[33]

Ranise, S. and Tinelli, C. The Satisfiability Modulo Theories Library (SMT-LIB), 2006; http://www.SMT-LIB.org

[34]

Tinelli, C. and Zarba, C.G. Combining nonstably infinite theories. Journal of Automated Reasoning 34, 3 (Apr. 2005), 209--238.

Digital Library

Cited By

Zheng LZhang KWei GChu H(2024)Mixed-Criticality Traffic Scheduling in Time-Sensitive Networking Using Multiple Combinatorial Packing Based on Free Time DomainElectronics10.3390/electronics1313264413:13(2644)Online publication date: 5-Jul-2024
https://doi.org/10.3390/electronics13132644
Murali VTrivedi AZamani M(2024)Falsification via Barrier Certificates2024 American Control Conference (ACC)10.23919/ACC60939.2024.10644795(4657-4662)Online publication date: 10-Jul-2024
https://doi.org/10.23919/ACC60939.2024.10644795
Wu NLi YYang HChen HDai SHao CYu CXie Y(2024)Survey of Machine Learning for Software-assisted Hardware Design Verification: Past, Present, and ProspectACM Transactions on Design Automation of Electronic Systems10.1145/366130829:4(1-42)Online publication date: 24-Apr-2024
https://dl.acm.org/doi/10.1145/3661308
Show More Cited By

Index Terms

Satisfiability modulo theories: introduction and applications

Recommendations

Solving SAT and SAT Modulo Theories: From an abstract Davis--Putnam--Logemann--Loveland procedure to DPLL(T)

We first introduce Abstract DPLL, a rule-based formulation of the Davis--Putnam--Logemann--Loveland (DPLL) procedure for propositional satisfiability. This abstract framework allows one to cleanly express practical DPLL algorithms and to formally reason ...
A tutorial on satisfiability modulo theories
CAV'07: Proceedings of the 19th international conference on Computer aided verification

Solvers for satisfiability modulo theories (SMT) check the satisfiability of first-order formulas containing operations from various theories such as the Booleans, bit-vectors, arithmetic, arrays, and recursive datatypes. SMT solvers are extensions of ...
A progressive simplifier for satisfiability modulo theories
SAT'06: Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing

In this paper we present a new progressive cooperating simplifier for deciding the satisfiability of a quantifier-free formula in the first-order theory of integers involving combinations of sublogics, referred to as Satisfiability Modulo Theories (SMT)...

Comments

Information & Contributors

Information

Published In

cover image Communications of the ACM

Communications of the ACM Volume 54, Issue 9

September 2011

121 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/1995376

Issue’s Table of Contents

Copyright © 2011 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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 2011

Published in CACM Volume 54, Issue 9

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Research-article
Popular
Refereed

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

430
Total Citations
View Citations
9,785
Total Downloads

Downloads (Last 12 months)1,407
Downloads (Last 6 weeks)175

Reflects downloads up to 22 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

Zheng LZhang KWei GChu H(2024)Mixed-Criticality Traffic Scheduling in Time-Sensitive Networking Using Multiple Combinatorial Packing Based on Free Time DomainElectronics10.3390/electronics1313264413:13(2644)Online publication date: 5-Jul-2024
https://doi.org/10.3390/electronics13132644
Murali VTrivedi AZamani M(2024)Falsification via Barrier Certificates2024 American Control Conference (ACC)10.23919/ACC60939.2024.10644795(4657-4662)Online publication date: 10-Jul-2024
https://doi.org/10.23919/ACC60939.2024.10644795
Wu NLi YYang HChen HDai SHao CYu CXie Y(2024)Survey of Machine Learning for Software-assisted Hardware Design Verification: Past, Present, and ProspectACM Transactions on Design Automation of Electronic Systems10.1145/366130829:4(1-42)Online publication date: 24-Apr-2024
https://dl.acm.org/doi/10.1145/3661308
Segovia-Ferreira MRubio-Hernan JCavalli AGarcia-Alfaro J(2024)A Survey on Cyber-Resilience Approaches for Cyber-Physical SystemsACM Computing Surveys10.1145/365295356:8(1-37)Online publication date: 26-Apr-2024
https://dl.acm.org/doi/10.1145/3652953
McGowen JDagli IDantam NBelviranli M(2024)Scheduling for Cyber-Physical Systems with Heterogeneous Processing Units under Real-World ConstraintsProceedings of the 38th ACM International Conference on Supercomputing10.1145/3650200.3656625(298-311)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3650200.3656625
Sundermann CHeß TSundermann RKuiter EKrieter SThüm T(2024)Generating Feature Models with UVL's Full ExpressivenessProceedings of the 28th ACM International Systems and Software Product Line Conference10.1145/3646548.3676602(61-65)Online publication date: 2-Sep-2024
https://dl.acm.org/doi/10.1145/3646548.3676602
Restrepo CRobin JMazo REgyed AWimmer MChechik MCombemale B(2024)Extensions and Scalability Experiments of a Generic Model-Driven Architecture for Variability Model ReasoningProceedings of the ACM/IEEE 27th International Conference on Model Driven Engineering Languages and Systems10.1145/3640310.3674090(126-137)Online publication date: 22-Sep-2024
https://dl.acm.org/doi/10.1145/3640310.3674090
Holzer SFrangoudis PTsigkanos CDustdar S(2024)SMT-as-a-Service for Fog-Supported Cyber-Physical SystemsProceedings of the 25th International Conference on Distributed Computing and Networking10.1145/3631461.3631562(154-163)Online publication date: 4-Jan-2024
https://dl.acm.org/doi/10.1145/3631461.3631562
Gundaram P(2024)Cryptanalysis of Selected ARX-Based Block CiphersVietnam Journal of Computer Science10.1142/S2196888824500143(1-16)Online publication date: 1-Jul-2024
https://doi.org/10.1142/S2196888824500143
Kuliamin V(2024)A Survey of Software Dynamic Analysis MethodsProgramming and Computing Software10.1134/S036176882401007950:1(90-114)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1134/S0361768824010079
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Digital Edition

View this article in digital edition.

Digital Edition

Magazine Site

View this article on the magazine site (external)

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Media

Figures

Other

Tables

View Issue’s Table of Contents