Computer Science – Discrete Mathematics
Scientific paper
2011-03-18
Fundamenta Informaticae, 2011, 109(1): pages 27-81, 83-119
Computer Science
Discrete Mathematics
91 pages, to appear in Fundamenta Informaticae, 2011, as Constraint satisfaction problems in clausal form I: Autarkies and def
Scientific paper
10.3233/FI-2011-428; 10.3233/FI-
This is the report-version of a mini-series of two articles on the foundations of satisfiability of conjunctive normal forms with non-boolean variables, to appear in Fundamenta Informaticae, 2011. These two parts are here bundled in one report, each part yielding a chapter. Generalised conjunctive normal forms are considered, allowing literals of the form "variable not-equal value". The first part sets the foundations for the theory of autarkies, with emphasise on matching autarkies. Main results concern various polynomial time results in dependency on the deficiency. The second part considers translations to boolean clause-sets and irredundancy as well as minimal unsatisfiability. Main results concern classification of minimally unsatisfiable clause-sets and the relations to the hermitian rank of graphs. Both parts contain also discussions of many open problems.
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