  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.
