Restricted Poly-Time SAT-Solvable CNF’s

This article, from an algorithmic point of view, studies the satisfiability problem SAT restricted to a CNF fraction MHF whose members consist of a Horn formula and a 2-CNF part. In general SAT is NP-complete for such formulas. We consider various structurally defined subclasses of MHF, for which SAT can be solved in polynomial time. The instances defined here are required to have a linear, or even exact-linear Horn part. Moreover, the 2-CNF part is required to be of specific graph structure, e.g., disjoint edges or disjoint triangles. Further poly-time classes are presented, for which the Horn part is not forced to be linear.