John V. Franco

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Two algorithms for the k-Satissability problem are presented and a probabilistic analysis is performed. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithms assign values to literals appearing in a given instance of k-Satissability, one at a time, until a solution is found(More)
An algorithm for the 3-Satissability problem is presented and a probabilistic analysis is performed. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithm assigns values to variables appearing in a given instance of 3-Satissability, one at a time, using the unit clause(More)
The scope of certain well-studied polynomial-time solvable classes of Satisfiability is investigated relative to a polynomial-time solvable class consisting of what we call matched formulas. The class of matched formulas has not been studied in the literature, probably because it seems not to contain many challenging formulas. Yet, we find that, in some(More)
In this note we present a simple quadratic-time algorithm for solving the satissability problem for a special class of boolean formulas. This class properly contains the class of extended Horn formulas 1] and balanced formulas 2, 4]. Previous algorithms for these classes require testing membership in the classes. However, the problem of recognizing balanced(More)
We consider pre-processing a random instance I of CNF Satissability in order to remove infrequent variables (those which appear once or twice in an instance) from I. The model used to generate random instances is the popular random-clause-sizemodel with parametersn, the number of clauses, r, the number of Boolean variables from which clauses are composed,(More)
Heusch introduced the notion of pure implicational formulas. He showed that the falsiiability problem for pure implicational formulas with k negations is solvable in time O(n k). Such falsiiability results are easily transformed to satissability results on CNF formulas. We show that the falsiiability problem for pure implicational formulas is solvable in(More)
The scope of certain well-studied polynomial-time solvable classes of Satis ability is investigated relative to a polynomial-time solvable class consisting of what we call matched formulas. The class of matched formulas has not been studied in the literature, probably because it seems not to contain many challenging formulas. Yet, we nd that, in some sense,(More)