Chapter 5 – Coverings of Automata

Publisher Summary This chapter discusses the coverings of automata. The chapter reviews Moore and Mealy machines. Simplicity of an automaton can be measured, for example, by the number of its states. Homomorphisms of automata, and homomorphism and covering are discussed. The admissible output-consistent decompositions, and reduction of covering of an automaton to covering of a semi-automaton are reviewed. Various theorems are proved in the chapter. Some properties of the notion of covering of semi-automata are derived. Construction of an auxiliary semi-automaton is reviewed. The chapter reviews the direct product of semi-automata, and the cascade product of semi-automata. The construction of a direct product can be, in an obvious way, generalized to any finite number of semi-automata with a common or appropriately translated set of inputs.