A Random Constraint Satisfaction Problem That Seems Hard for DPLL

Abstract. This paper discusses an NP-complete constraint satisfaction problem which appears to share many of the threshold characteristics of SAT but is similar to XOR-SAT and so is easier to analyze. For example, the exact satisfiability threshold for this problem is known, and the problem has high resolution complexity. In this paper, we prove the problem appears hard for DPLL. Specifically, if we pick a problem instance at random with constraint density higher than some given threshold but below the satisfiability threshold, a DPLL backtracking algorithm using the unit clause heuristic will, with uniformly positive probability, take exponential time to find a satisfying assignment.

• Type: Conference
• Year: 2004
• Where: SAT
• Authors: Harold S. Connamacher
• Keywords: Constraint Satisfaction Problem, Exact Satisfiability Threshold, SAT 2004, Satisfiability Threshold