A fixed point operator for the generalised maximum satisfiability problem

AbstractGiven an instance of the maximum satisfiability problem involving n logical variables, truth assignments naturally correspond to vertices of the n-hypercube. A discrete time dynamical system in Rn is described having the property that truth assignments which satisfy all clauses correspond to asymptotically stable fixed points, as well as do local optima. This result is established in the context of the “generalised maximum satisfiability problem”, defined as follows: Given a finite set of “components”, find a matching of each of them with one element of a finite set of “possible states”, in order to avoid as many a priori given conjunctions of states as possible. An algorithm for the maximum satisfiability problem is derived which qualitatively, on the basis of computational experiences, compares favorably with P. Hansen's SAMD descent ascent method.I don't see your problem, he said, no contradiction is involved when considering the catalog of activity reports mentioning themselves as activity of their own author ! He was right … on one point at least.fancy June 1989