A criterion for "easiness" of certain SAT problems

A generalized 1-in-3SAT problem is defined and found to be in complexity class P when restricted to a certain subset of CNF expressions. In particular, 1-in-kSAT with no restrictions on the number of literals per clause can be decided in polynomial time when restricted to exact READ-3 formulas with equal number of clauses (m) and variables (n), and no pure literals. Also individual instances can be checked for “easiness” with respect to a given SAT problem. By identifying whole classes of formulas as being solvable efficiently the approach might be of interest also in the complementary search for “hard” instances. Introduction. Many problems in propositional logic are varieties of the decision problem F SAT ? and are in complexity class NP. Examples are 1-in-3SAT which is the problem of deciding whether for a given 3CNF formula there exists an assignment which evaluates exactly one literal per clause to true, or NOT-ALL-EQUAL-3SAT which asks for an assignment with at least one true and one false literal per clause. Others, like e.g. HORN-SAT or 2-SAT, are known to be decidable in linear time and thus belong to complexity class P. For these and other examples see e.g. [1]. An extension of some of these NP problems to a more general requirement on the number of true literals and to instances where the number of literals in each clause is not restricted to exactly 3 will