  The complexity class DP is the class of all languages that are the
intersection of a language in NP and a language in co-NP, as coined by
Papadimitriou and Yannakakis (1982). Hartvigsen and Zemel (1992) conjectured
that recognizing a facet for the knapsack polytope is DP-complete. While it has
been known that the recognition problems of facets for polytopes associated
with other well-known combinatorial optimization problems, e.g., traveling
salesman, node/set packing/covering, are DP-complete, this conjecture on
recognizing facets for the knapsack polytope remains open. We provide a
positive answer to this conjecture. Moreover, despite the DP-hardness of the
recognition problem, we give a polynomial time algorithm for deciding if an
inequality with a fixed number of distinct positive coefficients defines a
facet of a knapsack polytope, generalizing a result of Balas (1975).
