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Deciding Disjunctive Linear Arithmetic with SAT

Ofer Strichman
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Abstract

Disjunctive Linear Arithmetic (DLA) is a major decidable theory that is supported by almost all existing theorem provers. The theory consists of Boolean combinations of predicates of the form $Σ_{j=1}^{n}a_j\cdot x_j \le b$, where the coefficients $a_j$, the bound $b$ and the variables $x_1 >... x_n$ are of type Real ($\mathbb{R}$). We show a reduction to propositional logic from disjunctive linear arithmetic based on Fourier-Motzkin elimination. While the complexity of this procedure is not better than competing techniques, it has practical advantages in solving verification problems. It also promotes the option of deciding a combination of theories by reducing them to this logic. Results from experiments show that this method has a strong advantage over existing techniques when there are many disjunctions in the formula.

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Ofer Strichman. 2004-02-01. Deciding Disjunctive Linear Arithmetic with SAT. https://arxiv.org/abs/cs/0402002

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