Finding Relations Among Linear Constraints

Abstract

In program analysis and verification, there are some constraints that have to be processed repeatedly. A possible way to speed up the processing is to find some relations among these constraints first. This paper studies the problem of finding Boolean relations among a set of linear numerical constraints. The relations can be represented by rules. It is believed that we can not generate all the rules in polynomial-time. A search based algorithm with some heuristics to speed up the search process is proposed. All the techniques are implemented in a tool called MALL which can generate the rules automatically. Experimental results with various examples show that our method can generate enough rules in acceptable time. Our method can also handle other types of constraints if proper numeric solvers are available.