Johnson, Papadimitriou and Yannakakis introduce the class $\PLS$ consisting of optimization problems for which efficient local- search heuristics exist. We formulate a type-2 problem $\iter$ that characterizes $\PLS$ in style of Beame et al., and prove a criterion for type-2 problems to be nonreducible to $\iter$. As a corollary, we ... more >>>