2010
DOI: 10.1007/s10817-010-9196-8
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SAT Modulo Linear Arithmetic for Solving Polynomial Constraints

Abstract: Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g., termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiabil… Show more

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Cited by 38 publications
(61 citation statements)
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“…for all n > 6, we finally conclude that Pólya and Szegö's representation is the best choice for an implementation using the constraint solving method in [5]: it minimizes both the number of variables V T (n) and formulas F T (n) to be considered.…”
Section: Comparisonmentioning
confidence: 79%
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“…for all n > 6, we finally conclude that Pólya and Szegö's representation is the best choice for an implementation using the constraint solving method in [5]: it minimizes both the number of variables V T (n) and formulas F T (n) to be considered.…”
Section: Comparisonmentioning
confidence: 79%
“…However, this does not pay attention to the subsequent constraint solving process that we need to use in any implementation. In [5] an efficient procedure to solve polynomial constraints C (e.g., P ≥ 0, where P is written as a sum of monomials with the corresponding coefficients) is given. The procedure transforms a polynomial constraint into a formula of the linear arithmetic and then fast, highly efficient Satisfiability Modulo Theories (SMT) techniques are used to find a solution.…”
Section: Quantitative Analysismentioning
confidence: 99%
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“…As a result, a nonlinear SMT formula is obtained, for which a model has to be found. Despite the great advances in non-linear SMT [9,10,11], the applicability of the approach is still strongly conditioned by current solving technology.…”
Section: Introductionmentioning
confidence: 99%
“…In spite of this theoretical limitation, and similarly to the real case, several methods that take advantage of the advancements in SAT and SMT solving have been proposed for solving integer polynomial constraints. The common idea of these methods is to reduce instances of integer non-linear arithmetic into problems of a simpler language that can be directly handled by existing SAT/SMT tools, e.g., propositional logic [24], linear bit-vector arithmetic [25], or linear integer arithmetic [26]. All these approaches are satisfiability-oriented, which makes them more convenient in contexts in which finding solutions is more relevant than proving that none exists (e.g., in invariant generation [27]).…”
Section: Introductionmentioning
confidence: 99%