The MathSAT5 SMT Solver

Cimatti, Alessandro; Griggio, Alberto; Schaafsma, Bastiaan Joost; Sebastiani, Roberto

doi:10.1007/978-3-642-36742-7_7

Cited by 389 publications

(258 citation statements)

References 21 publications

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“…We have implemented our approach over floating-point intervals inside the MATHSAT5 SMT solver [16]. We call our prototype tool FP-ACDCL.…”

Section: Implementation and Experimentsmentioning

confidence: 99%

“…For this, we have compared against all the SMT solvers supporting FPA that we were aware of, namely Z3 [26], SONOLAR [50] and MATHSAT5 [16]. All three solvers use a bit-vector encoding of floating-point arithmetic which is then solved via reduction to SAT(bit-blasting).…”

Section: Comparison With Bit-vector Encodingsmentioning

confidence: 99%

“…Recent decision procedures for floating-point logic are based on propositional encodings of floating-point constraints. Examples of this approach are implemented in MATHSAT5 [16], CBMC [17] and Sonolar [45]. A difficulty of this approach is that even simple floating-point formulas can have extremely large propositional encodings, which can be hard for current SAT solvers.…”

Section: Decision Proceduresmentioning

confidence: 99%

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Deciding floating-point logic with abstract conflict driven clause learning

Brain

D’Silva

Griggio

et al. 2013

Form Methods Syst Des

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We present a bit-precise decision procedure for the theory of floating-point arithmetic. The core of our approach is a non-trivial, lattice-theoretic generalisation of the conflict-driven clause learning algorithm in modern SAT solvers to lattice-based abstractions. We use floating-point intervals to reason about the ranges of variables, which allows us to directly handle arithmetic and is more efficient than encoding a formula as a bit-vector as in current floating-point solvers. Interval reasoning alone is incomplete, and we obtain completeness by developing a conflict analysis algorithm that reasons natively about intervals. We have implemented this method in the MATHSAT5 SMT solver and evaluated it on assertion checking problems that bound the values of program variables. Our new technique is faster than a bit-vector encoding approach on 80 % of the benchmarks, and is faster by one order of magnitude or more on 60 % of the benchmarks. The generalisation of CDCL we propose is widely applicable and can be used to derive abstraction-based SMT solvers for other theories.

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“…We have implemented our approach over floating-point intervals inside the MATHSAT5 SMT solver [16]. We call our prototype tool FP-ACDCL.…”

Section: Implementation and Experimentsmentioning

confidence: 99%

Section: Comparison With Bit-vector Encodingsmentioning

confidence: 99%

Section: Decision Proceduresmentioning

confidence: 99%

See 1 more Smart Citation

Deciding floating-point logic with abstract conflict driven clause learning

Brain

D’Silva

Griggio

et al. 2013

Form Methods Syst Des

Self Cite

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show abstract

“…This application happens before we start the branch-and-bound approach. We also compared our solver with state-of-the-art SMT solvers for linear integer arithmetic: cvc4-1.4 [1], mathsat5-3.13 [10], yices2.5.1 [13], and z3-4.4.1 [24]. All these solvers employ a branch-and-bound approach with an underlying dual simplex solver [14].…”

Section: Methodsmentioning

confidence: 99%

New techniques for linear arithmetic: cubes and equalities

Bromberger

Weidenbach

2017

Form Methods Syst Des

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We present several new techniques for linear arithmetic constraint solving. They are all based on the linear cube transformation, a method presented here, which allows us to efficiently determine whether a system of linear arithmetic constraints contains a hypercube of a given edge length. Our first findings based on this transformation are two sound tests that find integer solutions for linear arithmetic constraints. While many complete methods search along the problem surface for a solution, these tests use cubes to explore the interior of the problems. The tests are especially efficient for constraints with a large number of integer solutions, e.g., those with infinite lattice width. Inside the SMT-LIB benchmarks, we have found almost one thousand problem instances with infinite lattice width. Experimental results confirm that our tests are superior on these instances compared to several state-ofthe-art SMT solvers. We also discovered that the linear cube transformation can be used to investigate the equalities implied by a system of linear arithmetic constraints. For this purpose, we developed a method that computes a basis for all implied equalities, i.e., a finite representation of all equalities implied by the linear arithmetic constraints. The equality basis has several applications. For instance, it allows us to verify whether a system of linear arithmetic constraints implies a given equality. This is valuable in the context of NelsonOppen style combinations of theories.

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“…It is well known that SAT Modulo Theories (SMT) [20] solvers such as Mathsat5 [8], Yices [11], Z3 [10] or our own Barcelogic solver [6] mostly focus on efficiently handling the arbitrary Boolean structure on top of the LIA constraints. Their Theory Solver component, the one that handles conjunctions of constraints (our aim here), is rather basic, and we do not compere here with SMT solvers since on conjunctive problems they are indeed in general orders of magnitude worse than CPLEX or Gurobi.…”

Section: Methodsmentioning

confidence: 99%

The IntSat Method for Integer Linear Programming

Nieuwenhuis

2014

Lecture Notes in Computer Science

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Abstract. Conflict-Driven Clause-Learning (CDCL) SAT solvers can automatically solve very large real-world problems. To go beyond, and in particular in order to solve and optimize problems involving linear arithmetic constraints, here we introduce IntSat, a generalization of CDCL to Integer Linear Programming (ILP). Our simple 1400-line C++ prototype IntSat implementation already shows some competitiveness with commercial solvers such as CPLEX or Gurobi. Here we describe this new IntSat ILP solving method, show how it can be implemented efficiently, and discuss a large list of possible enhancements and extensions.

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The MathSAT5 SMT Solver

Cited by 389 publications

References 21 publications

Deciding floating-point logic with abstract conflict driven clause learning

Deciding floating-point logic with abstract conflict driven clause learning

New techniques for linear arithmetic: cubes and equalities

The IntSat Method for Integer Linear Programming

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