Accelerating tableaux proofs using compact representations

Abstract

In this article a modified form of tableau calculus, calledTableau Graph Calculus, is presented for overcoming the well-known inefficiencies of the traditional tableau calculus to a large extent. This calculus is based on a compact representation of analytic tableaux by using graph structures calledtableau graphs. These graphs are obtained from the input formula in linear time and incorporate most of the rule applications of normal tableau calculus during the conversion process. The size of this representation is linear with respect to the length of the input formula and the graph closely resembles the proof tree of tableau calculi thus retaining the naturalness of the proof procedure. As a result of this preprocessing step, tableau graph calculus has only a single rule which is repeatedly applied to obtain a proof. Many optimizations for the applications of this rule, to effectively prune the search space, are presented as well. Brief details of an implemented prover called FAUST, embedded within the higher-order theorem prover called HOL, are also given. Applications of FAUST within a hardware verification context are also sketched.