Deciding Equality Formulas by Small Domains Instantiations

We introduce an eecient decision procedure for the theory of equality based on nite instantiations. When using the nite instantiations method, it is a common practice to take a range of 1::n] (where n is the number of input non-Boolean variables) as the range for all non-Boolean variables, resulting in a state-space of n n. Although various attempts to minimize this range were made, typically they either required various restrictions on the investigated formulas or were not very eeective. In many cases, the n n state-space cannot be handled by BDD-based tools within a reasonable amount of time. In this paper we show that signiicantly smaller domains can be algorithmically found, by analyzing the structure of the formula. We also show an upper bound for the state-space based on this analysis. This method enabled us to verify formulas containing hundreds of integer and oating point variables.