Abstract
This chapter defines and represents a semi-automaton. Many physical devices have the remarkable property of tending to remain in any of a finite number of situations or states. The “jumping” from one state to another—sometimes the same—is a continuous process that must be very carefully considered by the designer of the device, but can be disregarded by the user interested only in various discrete states. Examples range from an electronic computer and chess play, through the inventory list of a factory and the distribution of manpower of a company, to traffic light and the ringing of a bell. The graph of a cyclic semi-automaton contains at least one vertex such that every vertex can be reached from it by a directed path, that is, a path following the arrows. The chapter reviews the homomorphisms of one-input semi-automata, and discusses the homomorphism of semigroups of homomorphic semi-automata.
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