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Finally, experimental results are presented. With these initial encouraging results, it is natural to test the NN on more naturally arising boolean expressions. The family of hamiltonian circuit problems provide a good source of interesting and hard SAT problems. The details and results of this work will be presented in the next section. 49 3. NP-COMPLETENESS The previous sections outline GA and NN paradigms for heuristically solving SAT problems. Experiments with simple boolean expressions are encouraging.

Second, the 28 application of a constraint satisfaction paradigm to SAT problems is described. The final section provides experimental results. 1. Overview Hinton [Hinton77] has shown that constraint satisfaction networks can be used to find near-optimal solutions to problems with a large set of simultaneous constraints. In such a paradigm, each node represents a hypothesis and each connection a constraint among two hypotheses. As an example, suppose that the nodes have binary activations (1 or -1) and are connected with symmetric weights.

Until this point, very little mention has been made of Biasi . In fact, it is only used to bias the root node to 1. Depending on the format of the boolean expression, however, it is sometimes possible to be sure of the activations of nodes other _________ than the root. For example, since the boolean expression (A AND ( B OR C )) must be true, it is a trivial task to deduce that A must be true, while B and C are false. The previous rules for bias are inadequate for expressing these new bias constraints.

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Algorithm for factorization of logic expressions by Fallah F


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