XORSAT: An Efficient Algorithm for the DIMACS 32-bit Parity Problem

TL;DR

The paper presents XORSAT, a new SAT solver for the DIMACS 32-bit parity problem, which significantly outperforms previous methods by splitting the problem and solving parts separately, achieving about 1000 times faster results.

Contribution

Introduces XORSAT, a novel solver that combines structured and random problem solving techniques, improving efficiency for the DIMACS 32-bit parity problem.

Findings

XORSAT solves the problem approximately 1000 times faster than EqSatz.

XORSAT reduces solving time from over 2800 seconds to under 3 seconds on tested instances.

The approach shows potential for application beyond the specific problem domain.

Abstract

The DIMACS 32-bit parity problem is a satisfiability (SAT) problem hard to solve. So far, EqSatz by Li is the only solver which can solve this problem. However, This solver is very slow. It is reported that it spent 11855 seconds to solve a par32-5 instance on a Maxintosh G3 300 MHz. The paper introduces a new solver, XORSAT, which splits the original problem into two parts: structured part and random part, and then solves separately them with WalkSAT and an XOR equation solver. Based our empirical observation, XORSAT is surprisingly fast, which is approximately 1000 times faster than EqSatz. For a par32-5 instance, XORSAT took 2.9 seconds, while EqSatz took 2844 seconds on Intel Pentium IV 2.66GHz CPU. We believe that this method significantly different from traditional methods is also useful beyond this domain.