A coterie, which is used to realize mutual exclusion in a distributed system is a family C of incomparable subsets such that every pair of subsets in C has at least one element in common. Associate with a family of subsets C a positive (i.e., monotone) Boolean function f/sub c/ such that f/sub c/(x)=1 if the Boolean vector x is equal to or greater than the characteristic vector of some subset in C, and 0 otherwise. It is known that C is a coterie if and only if f/sub c/ is dual-minor, and is a nondominated (ND) coterie if and only if f/sub c/ is self-dual. We introduce an operator /spl rho/, which transforms a positive self-dual function into another positive self-dual function, and the concept of almost-self-duality, which is a close approximation to self-duality and can be checked in polynomial time (the complexity of checking positive self-duality is currently unknown). After proving several interesting properties of them, we propose a simple algorithm to check whether a given positive function is self-dual or not. Although this is not a polynomial algorithm, it is practically efficient in most cases. Finally, we present an incrementally polynomial algorithm that generates all positive self-dual functions (ND coteries) by repeatedly applying p operations. Based on this algorithm, all ND coteries of up to seven variables are computed.>

A neural network for solving the traveling salesman problem (TSP) is proposed. The network is a modified version of the network suggested by J.J. Hopfield and O.W. Tank (1985) In the network of Hopfield and Tank, a neuron Ux,idenotes cityxoccupying positioniin the tour. This results in a network that, in general, is incapable of performing a shift in position for a number of adjacent cities, since this would temporarily increase the energy of the system. In the proposed network, a neuron Ux,yindicates whether or not citiesxandyare adjacent in the tour. An extra layer is added for the detection and elimination of closed subtours. This approach seems to have four major advantages: (a) computer simulations show a faster and more natural convergence of the network towards a configuration that represents a solution; (b) larger instances of the TSP can be solved readily; (c) the energy function is simplified; and (d) a general hardware implementation is possible because the distance terms occur only in the external inputs