SiCoTHEO—Simple competitive parallel theorem provers based on SETHEO

Abstract

In this paper, we present SiCoTHEO, a collection of parallel theorem provers for first order predicate logic. SiCoTHEO is based on the sequential prover SETHEO. Parallelism is exploited by competition: on each processor, an identical copy of SETHEO tries to prove the entire formula. However, certain parameters which influence SETHEO's behavior are set differently for each processor. As soon as one processor finds a proof, the entire system is stopped. Three different versions of SiCoTHEO are presented in this paper. We have used competition on completeness mode (parallel iterative deepening, SiCoTHEO-PID), on completeness bounds (a parameterized combination of bounds, SiCoTHEO-CBC), and on the search mode (top-down combined with bottom-up, SiCoTHEO-DELTA). The experimental results were obtained with a prototypical implementation, running on a network of workstations. This parallel model is fault-tolerant and does not need communication during run-time (except start and stop messages). We found that only little efficiency is gained for SiCoTHEO-PID, which reaches peak performance with only 4 processors. SiCoTHEO-CBC and SiCoTHEO-DELTA, however, showed significant speed-up, and improved performance up to the 50 processors used.