Cutting to the Chase

Jovanović, Dejan; Moura, Leonardo Mendonça de

doi:10.1007/s10817-013-9281-x

Cited by 22 publications

(65 citation statements)

References 19 publications

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“…We have found instances of polyhedra with the infinite lattice width property in some classes of the SMT-LIB benchmarks. These instances are 229 of the 233 dillig benchmarks designed by Dillig et al [11], 503 of the 591 CAV-2009 benchmarks also by Dillig et al [11], 229 of the 233 slacks benchmarks which are the dillig benchmarks extended with slack variables [18], and 19 of the 37 prime-cone benchmarks, that is, "a group of crafted benchmarks encoding a tight n-dimensional cone around the point whose coordinates are the first n prime numbers" [18]. The remaining problems (4 from dillig, 88 from CAV-2009, 4 from slacks, and 18 from prime-cone) do not have infinite lattice width because they are either tightly bounded or unsatisfiable.…”

Section: Methodsmentioning

confidence: 99%

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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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Section: Methodsmentioning

confidence: 99%

“…There exist alternative methods for solving linear integer constraints that do not rely on a branch-and-bound approach [6,18]. These have not yet matured enough to be competitive with our tests or state-of-the-art SMT theory solvers.…”

Section: Methodsmentioning

confidence: 99%

New techniques for linear arithmetic: cubes and equalities

Bromberger

Weidenbach

2017

Form Methods Syst Des

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“…On these grounds, the recent work by Jovanović and de Moura [13,14], although itself not terminating, constitutes an important step towards an algorithm that is both efficient and terminating. The termination does no longer rely on bounds that are a priori exponentially large in the occurring parameters.…”

Section: Introductionmentioning

confidence: 99%

“…CUTSAT [14] includes all of the rules of CUTSAT++ except for the rules Solve-Div-Left, Solve-Div-Right, and Resolve-Cooper, which are explained in more detail in Section 4.…”

Section: Introductionmentioning

confidence: 99%

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Linear Integer Arithmetic Revisited

Bromberger

Sturm

Weidenbach

2015

Automated Deduction - CADE-25

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Abstract. We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many stateof-the-art solvers neglect termination in favor of efficiency. It is challenging to design a solver that is both terminating and practically efficient. Recent work by Jovanović and de Moura constitutes an important step into this direction. Their algorithm CUTSAT is sound, but does not terminate, in general. In this paper we extend their CUTSAT algorithm by refined inference rules, a new type of conflicting core, and a dedicated rule application strategy. This leads to our algorithm CUTSAT++, which guarantees termination.

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Theory Combination: Beyond Equality Sharing

Bonacina

Fontaine

Ringeissen

et al. 2019

Lecture Notes in Computer Science

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Satisfiability is the problem of deciding whether a formula has a model. Although it is not even semidecidable in first-order logic, it is decidable in some first-order theories or fragments thereof (e.g., the quantifier-free fragment). Satisfiability modulo a theory is the problem of determining whether a quantifier-free formula admits a model that is a model of a given theory. If the formula mixes theories, the considered theory is their union, and combination of theories is the problem of combining decision procedures for the individual theories to get one for their union. A standard solution is the equality-sharing method by Nelson and Oppen, which requires the theories to be disjoint and stably infinite. This paper surveys selected approaches to the problem of reasoning in the union of disjoint theories, that aim at going beyond equality sharing, including: asymmetric extensions of equality sharing, where some theories are unrestricted, while others must satisfy stronger requirements than stable infiniteness; superposition-based decision procedures; and current work on conflict-driven satisfiability (CDSAT).

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Cutting to the Chase

Cited by 22 publications

References 19 publications

New techniques for linear arithmetic: cubes and equalities

New techniques for linear arithmetic: cubes and equalities

Linear Integer Arithmetic Revisited

Theory Combination: Beyond Equality Sharing

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