Hydra formulas and directed hypergraphs: A preliminary report
نویسندگان
چکیده
We consider the problem of determining minimal Horn formula size for a subclass of Horn formulas. A hydra formula is a Horn formula consisting of size 3 definite Horn clauses, specified by a set of bodies of size 2, and containing clauses formed by these bodies and all possible heads. A hydra formula can be specified by the undirected graph formed by the bodies occurring in the formula. Thus minimal formula size for hydras can be considered as a graph parameter, the hydra number. We discuss how the hydra number relates to other quantities such as the path cover number of the line graph, characterize trees with low hydra number and give bounds for the hydra number of complete binary trees. We also discuss a related optimization problem and formulate several open problems.
منابع مشابه
Hydras: Directed Hypergraphs and Horn Formulas
We introduce a new graph parameter, the hydra number, arising from the minimization problem for Horn formulas in propositional logic. The hydra number of a graph G = (V, E) is the minimal number of hyperarcs of the form u, v → w required in a directed hypergraph H = (V, F ), such that for every pair (u, v), the set of vertices reachable in H from {u, v} is the entire vertex set V if (u, v) ∈ E,...
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