### Compactly Generating All Satisfying Truth Assignments of a Horn Formula

#### Abstract

While it was known that all models of a Horn formula can be generated in output-polynomial time, here we present an explicit algorithm as opposed to the rather vague oracle-scheme suggested in the proof of [6, Thm.4]. It is an instance of some principle of exclusion that compactly (thus not one by one) generates all models of certain Boolean formulae given in CNF. The principle of exclusion can be adapted to generate only the models of weight k. We compare and contrast it with constraint programming, 0, 1 integer programming, and binary decision diagrams.

#### Keywords

Horn-models, output-polynomial algorithm, fixed-cardinality models

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