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Lazy Satisfiability Modulo Theories

Roberto Sebastiani
2007 Journal on Satisfiability, Boolean Modeling and Computation  
Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a first-order formula with respect to some decidable first-order theory T (SMT (T )).  ...  the boolean and the theory-specific components of reasoning.  ...  Introduction In this paper we present an extensive survey of Satisfiability Modulo Theories (SMT), with particular focus on the currently-most-effective approach to SMT, the lazy approach.  ... 
doi:10.3233/sat190034 fatcat:xtomk52xrvexxe75sloor4hdcm

From Propositional Satisfiability to Satisfiability Modulo Theories [chapter]

Hossein M. Sheini, Karem A. Sakallah
2006 Lecture Notes in Computer Science  
as Satisfiability Modulo Theories (SMT) problems.  ...  We will describe several combination strategies and their impact on scalability and performance of the overall solver in different settings and applications.  ...  Preliminaries Satisfiability Modulo Theories (SMT) is the problem of determining the satisfiability of a quantifier-free first-order logic (FOL) formula in one or more decidable theories.  ... 
doi:10.1007/11814948_1 fatcat:whtcmi5hejd7jf3ome2vhi64gi

Satisfiability Modulo Theories and Assignments [chapter]

Maria Paola Bonacina, Stéphane Graham-Lengrand, Natarajan Shankar
2017 Lecture Notes in Computer Science  
MCSAT lifted CDCL to SMT in the sense of satisfiability modulo a single theory T , which was instantiated to the theory of bit-vectors [19] and to non-linear integer arithmetic [8] .  ...  Applications typically require deciding the satisfiability of arbitrary quantifier-free formulae, or, equivalently, sets of ground clauses, in a combination T of theories T 1 , . . . , T n .  ...  This research was funded in part by NSF grants 1528153 and CNS-0917375, by DARPA under agreement number FA8750-16-C-0043, and by grant "Ricerca di base 2015" of the Università degli Studi di Verona.  ... 
doi:10.1007/978-3-319-63046-5_4 fatcat:ruo4tye77nb3nfo2tx355lgax4

Satisfiability Modulo Theories: An Appetizer [chapter]

Leonardo de Moura, Nikolaj Bjørner
2009 Lecture Notes in Computer Science  
Satisfiability Modulo Theories (SMT) is about checking the satisfiability of logical formulas over one or more theories.  ...  It also draws on the most prolific problems in the past century of symbolic logic: the decision problem, completeness and incompleteness of logical theories, and finally complexity theory.  ...  Given a theory T , we say ϕ is satisfiable modulo T if T ∪ {ϕ} is satisfiable. We use M |= T ϕ to denote M |= {ϕ} ∪ T .  ... 
doi:10.1007/978-3-642-10452-7_3 fatcat:wabzhnbstbcgphtptloaywgfxy

SMT-COMP: Satisfiability Modulo Theories Competition [chapter]

Clark Barrett, Leonardo de Moura, Aaron Stump
2005 Lecture Notes in Computer Science  
Of particular recent interest are solvers for Satisfiability Modulo Theories (SMT).  ...  The Satisfiability Modulo Theories Competition (SMT-COMP) is intended to spark further advances in the SMT field, especially for applications in verification.  ... 
doi:10.1007/11513988_4 fatcat:e4hzz64iubcd5pfroydoludhqa

Satisfiability modulo theory and binary puzzle

Putranto Utomo
2017 Journal of Physics, Conference Series  
Research concerning the satisfiability of formulas with respect to some background theory is called satisfiability modulo theory (SMT). An SMT solver is an extension of a satisfiability (SAT) solver.  ...  We look at the mathematical theory behind it.  ...  The satisfiability problem with these restrictions is called satisfiability modulo theory (SMT) [3] .  ... 
doi:10.1088/1742-6596/855/1/012057 fatcat:ngsek5pxf5bplo2umrjjtfe7py

A framework for Satisfiability Modulo Theories

Daniel Kroening, Ofer Strichman
2009 Formal Aspects of Computing  
We present a unifying framework for understanding and developing SAT-based decision procedures for Satisfiability Modulo Theories (SMT).  ...  Correspondence and offprint requests to: Ofer Strichman,  ...  We have presented a generic framework for propositional encoding of T -formulas starting from a deductive sound and complete decision procedure for a theory T .  ... 
doi:10.1007/s00165-009-0105-z fatcat:4uiuuhxm7jftvezwvg7gy6npjq

A Survey of Satisfiability Modulo Theory [article]

David Monniaux
2016 arXiv   pre-print
Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories.  ...  In this survey, we explain the combination of propositional satisfiability and decision procedures for conjunctions known as DPLL(T), and the alternative "natural domain" approaches.  ...  Introduction Satisfiability modulo theory (SMT) solving consists in deciding the satisfiability of a first-order formula with unknowns and relations lying in certain theories.  ... 
arXiv:1606.04786v1 fatcat:q3rzmjpndvdghfekeqe6vgkbq4

Computing Tropical Prevarieties with Satisfiability Modulo Theories (SMT) Solvers [article]

Christoph Lüders
2020 arXiv   pre-print
A novel way to use SMT (Satisfiability Modulo Theories) solvers to compute the tropical prevariety (resp. equilibrium) of a polynomial system is presented.  ...  It turns out that the SMT approach is faster than the polyhedral approach for models that would otherwise take more than one minute to compute, in many cases by a factor of 60 or more, and in the worst  ...  Satisfiability Modulo Theories (SMT) checking [15] is usually built on top of SAT (Boolean satisfiability), which is the first problem that was proved, in the form of 3SAT, to be NP-complete.  ... 
arXiv:2004.07058v3 fatcat:yhua4i5stvclzoutsggovt2rvi

A Survey of Satisfiability Modulo Theory [chapter]

David Monniaux
2016 Lecture Notes in Computer Science  
Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories.  ...  In this survey, we explain the combination of propositional satisfiability and decision procedures for conjunctions known as DPLL(T), and the alternative "natural domain" approaches.  ...  Introduction Satisfiability modulo theory (SMT) solving consists in deciding the satisfiability of a first-order formula with unknowns and relations lying in certain theories.  ... 
doi:10.1007/978-3-319-45641-6_26 fatcat:iqkvvrxgrnd6xgpqo3kenx6l7u

Personnel Scheduling as Satisfiability Modulo Theories

Christoph Erkinger, Nysret Musliu
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
In this paper, we propose a new exact approach to RWS that exploits the recent advances on Satisfiability Modulo Theories (SMT).  ...  Furthermore, we developed a new formulation based on bitvectors in order to achieve a more compact representation of the constraints and a reduced number of variables.  ...  Introduction For companies and organizations in a broad range of business areas, it is necessary to provide availability 24 hours a day and 7 days a week.  ... 
doi:10.24963/ijcai.2017/86 dblp:conf/ijcai/ErkingerM17 fatcat:icwlyaj6ojhopmmh7lbzwtl5he

A Tutorial on Satisfiability Modulo Theories [chapter]

Leonardo de Moura, Bruno Dutertre, Natarajan Shankar
2007 Lecture Notes in Computer Science  
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  ...  We briefly survey the theory of SAT and SMT solving, and present some of the key algorithms in the form of pseudocode.  ...  Such problems can be handled by solvers for theory satisfiability or satisfiability modulo theories (SMT).  ... 
doi:10.1007/978-3-540-73368-3_5 fatcat:scb4tuwskfh5tdo6m5tvbpb2yi

Efficient Satisfiability Modulo Theories via Delayed Theory Combination [chapter]

Marco Bozzano, Roberto Bruttomesso, Alessandro Cimatti, Tommi Junttila, Silvio Ranise, Peter van Rossum, Roberto Sebastiani
2005 Lecture Notes in Computer Science  
The problem of deciding the satisfiability of a quantifier-free formula with respect to a background theory, also known as Satisfiability Modulo Theories (SMT), is gaining increasing relevance in verification  ...  This approach is much simpler and natural, allows each of the solvers to be implemented and optimized without taking into account the others, and it nicely encompasses the case of non-convex theories.  ...  Satisfiability Modulo Theories Satisfiability Modulo a Theory is the problem of checking the satisfiability of a quantifierfree (or ground) first-order formula with respect to a given first-order theory  ... 
doi:10.1007/11513988_34 fatcat:2pahtwxsnzaznmsknb37ievqmq

A Progressive Simplifier for Satisfiability Modulo Theories [chapter]

Hossein M. Sheini, Karem A. Sakallah
2006 Lecture Notes in Computer Science  
referred to as Satisfiability Modulo Theories (SMT).  ...  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,  ...  Introduction Procedures to decide quantifier-free formulas in (a combination of) first-order theories, recently dubbed as Satisfiability Modulo Theories (SMT), have been used to solve problems in a wide  ... 
doi:10.1007/11814948_20 fatcat:wx36r3aqfvdz7pqj7f7otqerj4

Proof Checking Technology for Satisfiability Modulo Theories

Aaron Stump
2009 Electronical Notes in Theoretical Computer Science  
A common proof format for solvers for Satisfiability Modulo Theories (SMT) is proposed, based on the Edinburgh Logical Framework (LF).  ...  Two problems arise: checking very large proofs, and keeping proofs compact in the presence of complex side conditions on rules.  ...  Introduction At the heart of several current automated verification methods are automated reasoning tools for solving the problem of Satisfiability Modulo Theories (SMT).  ... 
doi:10.1016/j.entcs.2008.12.121 fatcat:diibgad3kffnla223fw52tycyq
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