Unconditional Lower Bounds for the Fredman--Khachiyan Algorithms for Monotone Boolean Duality Testing

We prove unconditional lower bounds on the number of recursive calls made by the two algorithms of Fredman and Khachiyan (1996) for monotone Boolean duality testing, as a function of the explicit input size $N$. For Algorithm A we show a lower bound of $N^{Ω(\log N)}$ on the dual pairs $(\HH_k,\LL_k