Journal of the ACM (JACM)
A parallel approach for theorem proving in propositional logic
Information Sciences: an International Journal
A simple parallel algorithm for finding a satisfying truth assignment to a 2-CNF formula
Information Processing Letters
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Computer Architecture and Parallel Processing
Computer Architecture and Parallel Processing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
A fast parallel algorithm for the maximal independent set problem
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
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In this paper, we present an efficient procedure for solving the theorem proving problem in propositional logic. To take advantage of vector processing, we develop a vectorized representation of the problem and the deductions are performed implicitly by simple AND and OR operations on vectors. The approach is simpler than those using explicit inference rules. Vectorized procedures based on the representation are then proposed. The computational bound of the approach on a concurrent-read exclusive-write parallel random access machine is of O(mlog"2n), where m is the number of clauses and n is the number of distinct Boolean variables in the given formula. A divide-and-conquer strategy is used to partition the problem so that it can be solved by the existing vector computers. Experiments are conducted on vector computers. The result confirms the effectiveness of vectorization techniques and applicability of vector processing to theorem proving in propositional logic.