A linear expected-time algorithm for deriving all logical conclusions implied by a set of Boolean inequalities. (English) Zbl 0596.90067

If R is a set of m binary relations on a set of n Boolean variables, then R may imply logical conclusion of the types: contradiction, fixation and identification. A way to derive all logical conclusions implied by R is to construct the logical closure \(\bar R\) of R and to scan all pairs of variables. The known algorithms for detecting all fixations require no less computations than to find \(\bar R\) of R, i.e. \(O(n^ 3)\). The algorithm proposed by the authors has a linear expected-time if the m relations of R are randomly chosen with a uniform probability among all binary relations. Computational experiments are also presented.
Reviewer: N.Y.Yanev


90C09 Boolean programming
Full Text: DOI


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