Using Clausal Graphs to Determine the Computational Complexity of k-Bounded Positive 1-in-3 SAT
نویسنده
چکیده
The 1-in-3 SAT problem is known to be NP-complete even in the absence of negated variables [1], a variant known as Positive (or Monotone) 1-in-3 SAT. In this note, we use clausal graphs to investigate a further restriction: kBounded-Positive 1-in-3 SAT (kBP 1-in-3 SAT), in which each variable occurs in no more than k clauses. We show that for k = 2, kBP 1-in-3 SAT is in the polynomial complexity class P, while for all k>2, it is NP-complete, providing another way of exploring the boundary between classes P and NP.
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