Experimental Evaluation of a Method to Simplify Expressions

Abstract: We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in practice, in spite of its great generality. We first recall the notion of a collection of structures, which allows us to manipulate very large (possibly infinite) sets of terms as a whole, i.e., without enumerating their elements. Then we use this tool to construct algorithms to simplify expressions. We give various reasons why it is difficult to make these algorithms precise and efficient. We then propose a number of approches to solve the raised issues. Finally, and importantly, we provide a detailed experimental evaluation of the method and a comparison of several variants of it. Although the method is completely generic, we use (arbitrary, not only two-level) boolean expressions as the application field for these experiments because impressive simplifications can be obtained in spite of the hardness of the problem.