On an Application of Dynamic Programming to the Synthesis of Logical Systems

In this paper we wish to initiate the study of the application of dynamic programming to the domain of problems arising in the synthesis of logical systems. In a number of fields one encounters the problem of converting a system in one state into another state in a most efficient fashion—in mathematical economics, in the theory of control processes, in network theory, and in trajectory processes. Here we wish to consider a type of question which arises in the design of computers and switching circuits. We shall first treat the problem in general terms, and then consider a special example to illustrate the methods.