Logical foundations of artificial intelligence
Logical foundations of artificial intelligence
Unification as a complexity measure for logic programming
Journal of Logic Programming
Information Processing Letters
Extended Horn sets in propositional logic
Journal of the ACM (JACM)
A hierarchy of tractable satisfiability problems
Information Processing Letters
On finding solutions for extended Horn formulas
Information Processing Letters
Renaming a Set of Clauses as a Horn Set
Journal of the ACM (JACM)
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A perspective on certain polynomial-time solvable classes of satisfiability
Discrete Applied Mathematics
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Complexity issues related to propagation completeness
Artificial Intelligence
Generalising Unit-Refutation Completeness and SLUR via Nested Input Resolution
Journal of Automated Reasoning
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Single look-ahead unit resolution (SLUR) algorithm is a nondeterministic polynomial time algorithm which for a given input formula in a conjunctive normal form (CNF) either outputs its satisfying assignment or gives up. A CNF formula belongs to the SLUR class if no sequence of nondeterministic choices causes the SLUR algorithm to give up on it. The SLUR class is reasonably large. It is known to properly contain the well studied classes of Horn CNFs, renamable Horn CNFs, extended Horn CNFs, and CC-balanced CNFs. In this paper we show that the SLUR class is considerably larger than the above mentioned classes of CNFs by proving that every Boolean function has at least one CNF representation which belongs to the SLUR class. On the other hand, we show, that given a CNF it is coNP-complete to decide whether it belongs to the SLUR class or not. Finally, we define a non-collapsing hierarchy of CNF classes SLUR(i ) in such a way that for every fixed i there is a polynomial time satisfiability algorithm for the class SLUR(i ), and that every CNF on n variables belongs to SLUR(i ) for some i ≤n .