Artificial Intelligence
A logical framework for default reasoning
Artificial Intelligence
A circumscriptive theorem prover
Proceedings of the 2nd international workshop on Non-monotonic reasoning
An incremental method for generating prime implicants/implicates
Journal of Symbolic Computation
CADE-10 Proceedings of the tenth international conference on Automated deduction
Optimizing the clausal normal form transformation
Journal of Automated Reasoning
Characterizing diagnoses and systems
Artificial Intelligence
Knowledge compilation and theory approximation
Journal of the ACM (JACM)
Switching and Finite Automata Theory: Computer Science Series
Switching and Finite Automata Theory: Computer Science Series
Fast Subsumption Checks Using Anti-Links
Journal of Automated Reasoning
Introduction to Logic and Switching Theory
Introduction to Logic and Switching Theory
Computing Prime Implicates Incrementally
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
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In this paper, an efficient recursive algorithm is presented to compute the set of prime implicants of a propositional formula in conjunctive normal form (CNF). The propositional formula is represented as a (0,1)-matrix, and a set of 1’s across its columns are termed as paths. The algorithm finds the prime implicants as the prime paths in the matrix using the divide-and-conquer technique. The algorithm is based on the principle that the prime implicant of a formula is the concatenation of the prime implicants of two of its subformulae. The set of prime paths containing a specific literal and devoid of a literal are characterized. Based on this characterization, the formula is recursively divided into subformulae to employ the divide-and-conquer paradigm. The prime paths of the subformulae are then concatenated to obtain the prime paths of the formula. In this process, the number of subsumption operations is reduced. It is also shown that the earlier algorithm based on prime paths has some avoidable computations that the proposed algorithm avoids. Besides being more efficient, the proposed algorithm has the additional advantage of being suitable for the incremental method, without recomputing prime paths for the updated formula. The subsumption operation is one of the crucial operations for any such algorithms, and it is shown that the number of subsumption operation is reduced in the proposed algorithm. Experimental results are presented to substantiate that the proposed algorithm is more efficient than the existing algorithms.