Abstract
Consider a setR ofm binary relations on a set ofn boolean variables.R may imply a contradiction, the fixation of some variables at 0 or at 1 and/or the identification of some pairs of variables in direct or complemented form. An O(n) expected-time algorithm is given for the derivation of all such logical conclusions. Computational experiments with problems involving up to 2000 variables are reported on. The proposed algorithm is more than 100 times faster than previous methods whenn ≥ 100.
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On leave from Faculté Universitaire Catholique de Mons, Belgium. Written at CNRS, LAMSADE. Support of CNRS is gratefully acknowledged.
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Hansen, P., Jaumard, B. & Minoux, M. A linear expected-time algorithm for deriving all logical conclusions implied by a set of boolean inequalities. Mathematical Programming 34, 223–231 (1986). https://doi.org/10.1007/BF01580586
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DOI: https://doi.org/10.1007/BF01580586