201. Incorporating Dilemma Reasoning into Modern SAT Solvers
- Author
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Yue Chen Li, Kian Ming A. Chai, and Vincent Boon Chin Seng
- Subjects
Dilemma ,Vertex (graph theory) ,Theoretical computer science ,Computer science ,Decomposition tree ,Parallel algorithm ,Decomposition method (constraint satisfaction) ,Solver ,Boolean satisfiability problem ,Knowledge sharing - Abstract
The Boolean SATisfiability Problem (SAT) is an important intractable problem in computer science with numerous theoretical and industrial applications. With the growing availability of multi-core and multi-processor systems, parallel algorithms are increasingly important and useful. Yet, state-of-the-art parallel SAT solvers are mostly portfolio solvers that exchange learn’t clauses to achieve knowledge sharing. We describe some novel extensions to using Stalmarck’s method to create a parallel SAT solver. This includes two new knowledge sharing methods across solvers, t-BFD and c-BFD merging. We prove that t-BFD and c-BFD merging are distinct, and experimentally show that they occur significantly. In fact, t-BFD merging occurs more frequently at deeper levels of the problem decomposition tree. Within the problem subtree, t-BFDs merging gives unit clauses, and c-BFD merging gives clauses that are empirically short. Such short clauses are likely useful in simplifying the problem. Also, we introduce a more flexible problem decomposition method than naive splitting on N variables to form \(2^N\) subproblems. Based on the Dilemma Rule, it picks branching literals independently at every vertex in the decomposition tree. In addition, we engineered a method to avoid processor starvation in the parallelisation. We benchmarked a preliminary implementation of our modified solver against Glucose-Syrup 4.1 and show that certain configurations of restart and runtime budgets allow our solver to outperform Glucose-Syrup 4.1 on SAT instances. Furthermore, t-BFD merging significantly improved our solver’s performance on UNSAT benchmarks, suggesting that t-BFD and c-BFD merging are effective.
- Published
- 2021