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- W52037912 abstract "An algorithm for generating all of the models of a Boolean expression is presented. This constraint calculus assumes that an expression evaluates to True, reverse-evaluates the expression, and uses the consequences of this assumption to generate models. The constraint calculus is proven to be sound and complete. An algorithm for determining the satisfiability of Boolean expressions is derived from the constraint calculus. Neither the constraint calculus nor the satisfiability-determination (SD) algorithm require that an expression be in either Conjunctive or Disjunctive Normal Form.The constraint tree, one of the intermediate data structures constructed by the SD algorithm, is an excellent site for applying enhancements to the basic algorithm. An Elegant Normal Form for constraint trees is presented. Reducing a constraint tree to elegance before completing the satisfiability test should reduce the need for backtracking during the last stage of the test. Eight constraint-tree transformations are introduced and are proven to be a complete set of reductions for reducing constraint trees to elegance. A Reduction-To-Elegance (RTE) algorithm is presented.A method for randomly generating sets of expressions is discussed. The results of applying the SD and RTE algorithms to 300,000 randomly-generated expressions having from 100 to 500 literals each are presented. Under the unaugmented SD algorithm, 99.9% of the expressions had their satisfiability determined by visiting fewer than 1000 nodes during the final stage of the algorithm, and only 16% required backtracking. Under the SD algorithm augmented by the RTE algorithm, 99.99% of the expressions had their satisfiability determined by visiting fewer than 100 nodes, and only 1% required backtracking. 99% of the elegant expressions which were reconstructed from elegant constraint trees had fewer than 3% of their original literals, and all of the elegant expressions had fewer than 10% of their original literals. All of the contradictions and 99.99% of the tautologies were recognized by the RTE algorithm.The SD and RTE algorithms are two components of an expert system for satisfiability testing which may be used to simplify Boolean expressions used in circuit design, and to facilitate the solution of instances of other NP-complete problems." @default.
- W52037912 created "2016-06-24" @default.
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- W52037912 date "1990-01-01" @default.
- W52037912 modified "2023-09-26" @default.
- W52037912 title "Elements of an expert system for determining the satisfiability of general Boolean expressions" @default.
- W52037912 hasPublicationYear "1990" @default.
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