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Efficient Preprocessing Methods for Quantifier Elimination

机译:消除量词的高效预处理方法

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This paper presents a framework and prototype implementation for preprocessing quantified input formulas that are intended as input for quantifier elimination algorithms. The framework loosely follows the AI search paradigm — exploring the space of formulas derived from the input by applying various rewriting operators in search of a problem formulation that will be good input for the intended Q.E. program. The only operator provided by the prototype implementation presented here is substitution for variables constrained by equations in which they appear linearly, supported by factorization and a simple check for non-vanishing of denominators in substitutions. Yet we present examples of quantified formulas which can be reduced by our preprocessing method to problems solvable by current quantifier elimination packages, whereas the original formulas had been inaccessible to those.
机译:本文介绍了用于预处理量化输入公式的框架和原型实现,这些输入公式旨在用作量词消除算法的输入。该框架松散地遵循了AI搜索范式-通过应用各种重写运算符来搜索将成为预期Q.E良好输入的问题公式,从而探索从输入得出的公式的空间。程序。这里介绍的原型实现提供的唯一运算符是替换受方程式约束的变量,这些变量在其中线性出现,并通过分解进行分解,并简单检查替换中的分母是否消失。但是,我们提供了一些量化公式的示例,这些示例可以通过我们的预处理方法简化为当前的量化器消除程序包可以解决的问题,而原始公式对于这些公式来说是不可访问的。

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