Initial Automata

Abstract

In this chapter we will extend our theory to automata with fixed initial state, called initial automata. The initial state will be given by a K-morphism a:U → S where U is the unit object in the monoidal category (K,⊗,U) and S the state object of an automaton. If A is a deterministic type automaton and U ={1} the initial state is for example defined by a(1)∈S. The behavior of an initial automaton is defined as being the input-output morphism of the initial state.