An Algorithm for the Class of Pure Implicational Formulas

Heusch introduced the notion of pure implicational formulas. He showed that the falsiiability problem for pure implicational formulas with k negations is solvable in time O(n k). Such falsiiability results are easily transformed to satissability results on CNF formulas. We show that the falsiiability problem for pure implicational formulas is solvable in time O(k k n 2), which is polynomial for a xed k. Thus this problem is xed-parameter tractable.