Annotation: In the paper some machine-learning method for synthesis an on-fly event acceptor is proposed. Such an acceptor appears to be necessary for the technique of the on-fly event processing. This approach is increasingly being used in the design of real-time control and monitoring systems. In the paper the synthesis problem for such an acceptor is considered in a rigorous mathematical formulation. The method for solution of the problem and the computer experiment to study the method are described. The directions for the further research are proposed.