PHASE TRANSITIONS OF EXPSPACE-COMPLETE PROBLEMS

Abstract

This paper explores the phase transitions of the EXPSPACE-complete problems, which mainly focus on the conformant planning problems. The research presents two conformant planning algorithms—CONFORMANT PLAN-NONEXISTENCE algorithm and CONFORMANT PLAN-EXISTENCE algorithm. By analyzing the features of the two algorithms, the phase transition area of the conformant planning problems is obtained. If the number of the operators isn't greater than θub, the CONFORMANT PLAN-NONEXISTENCE algorithm can prove that nearly all the conformant planning instances have no solution. If the number of the operators isn't lower than θlb, the CONFORMANT PLAN-EXISTENCE algorithm can prove that nearly all the conformant planning instances have solutions. The results of the experiments show that there exist phase transitions from a region where almost all the conformant planning instances have no solution to a region where almost all the conformant planning instances have solutions.