1,967 research outputs found
A Survey of Satisfiability Modulo Theory
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. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
On Relation between Constraint Answer Set Programming and Satisfiability Modulo Theories
Constraint answer set programming is a promising research direction that
integrates answer set programming with constraint processing. It is often
informally related to the field of satisfiability modulo theories. Yet, the
exact formal link is obscured as the terminology and concepts used in these two
research areas differ. In this paper, we connect these two research areas by
uncovering the precise formal relation between them. We believe that this work
will booster the cross-fertilization of the theoretical foundations and the
existing solving methods in both areas. As a step in this direction we provide
a translation from constraint answer set programs with integer linear
constraints to satisfiability modulo linear integer arithmetic that paves the
way to utilizing modern satisfiability modulo theories solvers for computing
answer sets of constraint answer set programs.Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
Adapting Real Quantifier Elimination Methods for Conflict Set Computation
The satisfiability problem in real closed fields is decidable. In the context
of satisfiability modulo theories, the problem restricted to conjunctive sets
of literals, that is, sets of polynomial constraints, is of particular
importance. One of the central problems is the computation of good explanations
of the unsatisfiability of such sets, i.e.\ obtaining a small subset of the
input constraints whose conjunction is already unsatisfiable. We adapt two
commonly used real quantifier elimination methods, cylindrical algebraic
decomposition and virtual substitution, to provide such conflict sets and
demonstrate the performance of our method in practice
Applying SMT Solvers to the Test Template Framework
The Test Template Framework (TTF) is a model-based testing method for the Z
notation. In the TTF, test cases are generated from test specifications, which
are predicates written in Z. In turn, the Z notation is based on first-order
logic with equality and Zermelo-Fraenkel set theory. In this way, a test case
is a witness satisfying a formula in that theory. Satisfiability Modulo Theory
(SMT) solvers are software tools that decide the satisfiability of arbitrary
formulas in a large number of built-in logical theories and their combination.
In this paper, we present the first results of applying two SMT solvers, Yices
and CVC3, as the engines to find test cases from TTF's test specifications. In
doing so, shallow embeddings of a significant portion of the Z notation into
the input languages of Yices and CVC3 are provided, given that they do not
directly support Zermelo-Fraenkel set theory as defined in Z. Finally, the
results of applying these embeddings to a number of test specifications of
eight cases studies are analysed.Comment: In Proceedings MBT 2012, arXiv:1202.582
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