SAT modulo linear arithmetic for Solving Polynomial Constraints

Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g.; termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints ba...

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Autores: Borralleras, Cristina, Oliveras, Albert, Rodriguez-Carbonell, Enric, Rubio, Albert, Lucas Alba, Salvador|||0000-0001-9923-2108
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/37666
Acceso en línea:https://riunet.upv.es/handle/10251/37666
Access Level:acceso abierto
Palabra clave:Constraint solving
Non-linear arithmetic
Polynomial constraints
SAT modulo theories
System verification
Termination
Hardware and software
Linear arithmetic
Non-linear constraints
Program invariants
Satisfiability
System verifications
Unsatisfiable core
Formal logic
Hybrid systems
Polynomials
Verification
LENGUAJES Y SISTEMAS INFORMATICOS
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spelling SAT modulo linear arithmetic for Solving Polynomial ConstraintsBorralleras, CristinaOliveras, AlbertRodriguez-Carbonell, EnricRubio, AlbertLucas Alba, Salvador|||0000-0001-9923-2108Constraint solvingNon-linear arithmeticPolynomial constraintsSAT modulo theoriesSystem verificationTerminationHardware and softwareLinear arithmeticNon-linear constraintsProgram invariantsSatisfiabilitySystem verificationsUnsatisfiable coreFormal logicHybrid systemsPolynomialsVerificationLENGUAJES Y SISTEMAS INFORMATICOSPolynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g.; termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiability, which is more relevant in several applications as we illustrate with several examples. Nevertheless, we also present new techniques based on the analysis of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad class of problems. The power of our approach is demonstrated by means of extensive experiments comparing our prototype with state-of-the-art tools on benchmarks taken both from the academic and the industrial world. © 2010 Springer Science+Business Media B.V.This work has been partially supported by the EU (FEDER) and the Spanish MEC/MICINN, under grants TIN 2007-68093-C02-01 and TIN 2007-68093-C02-02.Springer NetherlandsDepartamento de Sistemas Informáticos y ComputaciónEscuela Técnica Superior de Ingeniería InformáticaInstituto Universitario Valenciano de Investigación en Inteligencia ArtificialMinisterio de Educación y CienciaRepositorio Institucional de la Universitat Politècnica de València Riunet20122012-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/37666reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Educación y Ciencia https://doi.org/10.13039/501100008743 TIN2007-68093-C02-02 TECHNOLOGICS-UPVMinisterio de Educación y Ciencia https://doi.org/10.13039/501100008743 TIN2007-68093-C02-01 LOGICTOOLS-2open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/376662026-06-13T07:49:27Z
dc.title.none.fl_str_mv SAT modulo linear arithmetic for Solving Polynomial Constraints
title SAT modulo linear arithmetic for Solving Polynomial Constraints
spellingShingle SAT modulo linear arithmetic for Solving Polynomial Constraints
Borralleras, Cristina
Constraint solving
Non-linear arithmetic
Polynomial constraints
SAT modulo theories
System verification
Termination
Hardware and software
Linear arithmetic
Non-linear constraints
Program invariants
Satisfiability
System verifications
Unsatisfiable core
Formal logic
Hybrid systems
Polynomials
Verification
LENGUAJES Y SISTEMAS INFORMATICOS
title_short SAT modulo linear arithmetic for Solving Polynomial Constraints
title_full SAT modulo linear arithmetic for Solving Polynomial Constraints
title_fullStr SAT modulo linear arithmetic for Solving Polynomial Constraints
title_full_unstemmed SAT modulo linear arithmetic for Solving Polynomial Constraints
title_sort SAT modulo linear arithmetic for Solving Polynomial Constraints
dc.creator.none.fl_str_mv Borralleras, Cristina
Oliveras, Albert
Rodriguez-Carbonell, Enric
Rubio, Albert
Lucas Alba, Salvador|||0000-0001-9923-2108
author Borralleras, Cristina
author_facet Borralleras, Cristina
Oliveras, Albert
Rodriguez-Carbonell, Enric
Rubio, Albert
Lucas Alba, Salvador|||0000-0001-9923-2108
author_role author
author2 Oliveras, Albert
Rodriguez-Carbonell, Enric
Rubio, Albert
Lucas Alba, Salvador|||0000-0001-9923-2108
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Departamento de Sistemas Informáticos y Computación
Escuela Técnica Superior de Ingeniería Informática
Instituto Universitario Valenciano de Investigación en Inteligencia Artificial
Ministerio de Educación y Ciencia
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Constraint solving
Non-linear arithmetic
Polynomial constraints
SAT modulo theories
System verification
Termination
Hardware and software
Linear arithmetic
Non-linear constraints
Program invariants
Satisfiability
System verifications
Unsatisfiable core
Formal logic
Hybrid systems
Polynomials
Verification
LENGUAJES Y SISTEMAS INFORMATICOS
topic Constraint solving
Non-linear arithmetic
Polynomial constraints
SAT modulo theories
System verification
Termination
Hardware and software
Linear arithmetic
Non-linear constraints
Program invariants
Satisfiability
System verifications
Unsatisfiable core
Formal logic
Hybrid systems
Polynomials
Verification
LENGUAJES Y SISTEMAS INFORMATICOS
description Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g.; termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiability, which is more relevant in several applications as we illustrate with several examples. Nevertheless, we also present new techniques based on the analysis of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad class of problems. The power of our approach is demonstrated by means of extensive experiments comparing our prototype with state-of-the-art tools on benchmarks taken both from the academic and the industrial world. © 2010 Springer Science+Business Media B.V.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/37666
url https://riunet.upv.es/handle/10251/37666
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Educación y Ciencia https://doi.org/10.13039/501100008743 TIN2007-68093-C02-02 TECHNOLOGICS-UPV
Ministerio de Educación y Ciencia https://doi.org/10.13039/501100008743 TIN2007-68093-C02-01 LOGICTOOLS-2
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Netherlands
publisher.none.fl_str_mv Springer Netherlands
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301629

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