Accelerating Tableaux Proofs Using Compact Representations

In this article a modiied form of tableau calculus, called Tableau Graph Calculus, is presented for overcoming the well-known ineeciencies of the traditional tableau calculus to a large extent. This calculus is based on a compact representation of analytic tableaux by using graph structures called tableau 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 eeectively 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 veriication context are also sketched.