Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Inference with path resolution and semantic graphs
Journal of the ACM (JACM)
Artificial Intelligence
An algorithm to compute circumscription
Artificial Intelligence
An incremental method for generating prime implicants/implicates
Journal of Symbolic Computation
CADE-10 Proceedings of the tenth international conference on Automated deduction
Characterizing diagnoses and systems
Artificial Intelligence
Theoretical Computer Science
Dissolution: making paths vanish
Journal of the ACM (JACM)
SETHEO: a high-performance theorem prover
Journal of Automated Reasoning
On the size of binary decision diagrams representing Boolean functions
Theoretical Computer Science
Non-Clausal Deductive Techniques for Computing Prime Implicants and Prime Implicates
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
Computing Prime Implicates Incrementally
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
An Efficient Algorithm to Generate Prime Implicants
Journal of Automated Reasoning
An Open Research Problem: Strong Completeness of R. Kowalski's Connection Graph Proof Procedure
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II
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The concept of anti-link is defined (an anti-link consists of two occurrences of the same literal in a formula), and useful equivalence-preserving operations based on anti-links are introduced. These operations eliminate a potentially large number of subsumed paths in a negation normal form formula. Those anti-links that directly indicate the presence of subsumed paths are characterized. The operations have linear time complexity in the size of that part of the formula containing the anti-link.The problem of removing all subsumed paths in an NNF formula is shown to be NP-hard, even though such formulas may be small relative to the size of their path sets. The general problem of determining whether there exists a pair of subsumed paths associated with an arbitrary anti-link is shown to be NP-complete. Additional techniques that generalize the concept of pure literals are introduced and are also shown to eliminate redundant subsumption checks. The effectiveness of these techniques is examined with respect to some benchmark examples from the literature.