On-Line Algorithms for Satisfiability Problems with Uncertainty

In this paper the problem of the on-line satisfiability of a Horn formula with uncertainty is addressed; we show how to represent a significant class of formulae by weighted directed hypergraphs and we present two algorithms that solve the on-line SAT problem and find a minimal interpretation for the formula working on the dynamic hypergraph representation. These algorithms make increasing assumptions on the formula and we will find that the second one solves the on-line SAT problem with a total time linear in the size of the formula, matching the optimal result for boolean Horn formulae.

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