-"""'-"- 31 5

that by enlarging the memory and processing more data as they come in, an acceleration of the rate of convergence can be obtaine~. The probabilistic search procedure presented here does not have these disadvantages. After proving the optimality of our procedure, both the convergence as it is defined for other random search procedures [14]-[16] and the convergences of state functions of interest in automata theory [I ]-[4] are discussed. It is emphasized that the algorithm can easily cope with high noise and large strategy number situations. There is a great deal of freedom left to the designer within the boundaries dictated by the conditions of convergence. This freedom can be used to obtain fast-converging schemes. It is indicated how the algorithm can be modified to operate in nonstationary environments. This modified procedure will be proved to be t-optimal with respect to a certain function of the search parameters. Later on, the organizational aspect of the search is briefly treated, and a specific design of the scheme is experimentally tested on the test problem of Shapiro and Narendra [6]. The rate of convergence for this scheme is considerably higher than for the SA VS, although further comparisons between the two techniques seem necessary.