An algorithm for the class of pure implicational formulas

Heusch introduced the notion of pure implicational formulas. He showed that the falsifiability problem for pure implicational formulas with k negations is solvable in time O(n(k)). Such falsifiability results are easily transformed to satisfiability results on CNF formulas. We show that the falsifiability problem for pure implicational formulas is solvable in time O(k(k)n(2)), which is polynomial for a fixed k. Thus this problem is fixed-parameter tractable. (C) 1999 Elsevier Science B.V. All rights reserved.