Book ChapterDOI
Satisfiability Modulo Theories
Clark Barrett,Cesare Tinelli +1 more
- pp 305-343
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TLDR
The architecture of a lazy SMT solver is discussed, examples of theory solvers are given, how to combine such solvers modularly is shown, and several extensions of the lazy approach are mentioned.Abstract:
Satisfiability Modulo Theories (SMT) refers to the problem of determining whether a first-order formula is satisfiable with respect to some logical theory. Solvers based on SMT are used as back-end engines in model-checking applications such as bounded, interpolation-based, and predicate-abstraction-based model checking. After a brief illustration of these uses, we survey the predominant techniques for solving SMT problems with an emphasis on the lazy approach, in which a propositional satisfiability (SAT) solver is combined with one or more theory solvers. We discuss the architecture of a lazy SMT solver, give examples of theory solvers, show how to combine such solvers modularly, and mention several extensions of the lazy approach. We also briefly describe the eager approach in which the SMT problem is reduced to a SAT problem. Finally, we discuss how the basic framework for determining satisfiability can be extended with additional functionality such as producing models, proofs, unsatisfiable cores, and interpolants.read more
Citations
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Tools and Algorithms for the Construction and Analysis of Systems. Proc. TACAS 2009
Stefan Kowalewski,Anna Philippou +1 more
TL;DR: This paper presents a meta-modelling framework for modeling and testing the robustness of the modeled systems and some of the techniques used in this framework have been developed and tested in the field.
Book ChapterDOI
Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks
TL;DR: In this paper, the authors presented a scalable and efficient technique for verifying properties of deep neural networks (or providing counter-examples) based on the simplex method, extended to handle the non-convex Rectified Linear Unit (ReLU) activation function.
The SMT-LIB Standard Version 2.0
TL;DR: This paper introduces Version 2 of the SMT-LIB Standard, a major upgrade of the previous Version 1.2 which, in addition to simplifying and extending the languages of that version, includes a new command language for interfacing with SMT solvers.
Journal Article
Interpolation and SAT-based model checking
TL;DR: In benchmark studies using a set of large industrial circuit verification instances, this method is greatly more efficient than BDD-based symbolic model checking, and compares favorably to some recent SAT-based model checking methods on positive instances.
Journal ArticleDOI
Formal methods: Practice and experience
TL;DR: The state of the art in the industrial use of formal methods is described, concentrating on their increasing use at the earlier stages of specification and design, by comparing the situation in 2009 with the most significant surveys carried out over the last 20 years.
References
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Book ChapterDOI
Z3: an efficient SMT solver
TL;DR: Z3 is a new and efficient SMT Solver freely available from Microsoft Research that is used in various software verification and analysis applications.
Journal ArticleDOI
A new polynomial-time algorithm for linear programming
TL;DR: It is proved that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property: the ratio of the radius of the smallest sphere with center a′, containingP′ to theradius of the largest sphere withCenter a′ contained inP′ isO(n).
Book
A machine program for theorem-proving
TL;DR: The programming of a proof procedure is discussed in connection with trial runs and possible improvements.
Book ChapterDOI
An Extensible SAT-solver
Niklas Een,Niklas Sörensson +1 more
TL;DR: This article presents a small, complete, and efficient SAT-solver in the style of conflict-driven learning, as exemplified by Chaff, and includes among other things a mechanism for adding arbitrary boolean constraints.