非线性整数算术推理的协同框架

2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing Pub Date : 2013-09-23 DOI:10.1109/SYNASC.2013.29

S. Conchon, Mohamed Iguernelala, A. Mebsout

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引用次数: 9

摘要

本文描述了一个用于非线性整数算法简单性质模推理的协作框架。该框架依赖于AC(X)组合方法和区间微积分。第一部分用于处理线性整数算术等式和非线性乘法的结合性和交换性。除了对不等式的标准线性运算之外，还使用了区间微积分组件来细化非线性项的边界，并告知SAT求解器在有界区间上的明智的情况分裂。该框架已在Alt-Ergo定理证明器中实现。我们在演绎程序验证生成的一组公式上证明了它的有效性。

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A Collaborative Framework for Non-Linear Integer Arithmetic Reasoning in Alt-Ergo

In this paper, we describe a collaborative framework for reasoning modulo simple properties of non-linear integer arithmetic. This framework relies on the AC(X) combination method and on interval calculus. The first component is used to handle equalities of linear integer arithmetic and associativity and commutativity properties of non-linear multiplication. The interval calculus component is used - in addition to standard linear operations over inequalities - to refine bounds of non-linear terms and to inform the SAT solver about judicious case-splits on bounded intervals. The framework has been implemented in the Alt-Ergo theorem prover. We show its effectiveness on a set of formulas generated from deductive program verification.

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2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

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