On the fixed-parameter tractability of the equivalence test of monotone normal forms

We consider the problem Monet—given two monotone formulas φ in DNF and ψ in CNF, decide whether they are equivalent. While Monet is probably not coNP-hard, it is a long standing open question whether it has a polynomial time algorithm and thus belongs to P. In this paper we examine the parameterized complexity of Monet. We show that Monet is in FPT by giving fixed-parameter algorithms for different parameters.