I don't know how this word got missing, and why we didn't notice it before.
I remember we discussed these definition in Brno when we were writing the first draft, and that I had to dig up several papers to prove that these definitions are used.
In a complete automaton there always exists a way to read any letter letter α from any state s, so |δ(s,α)|≥1. In a deterministic automaton there is at most one way to do so: |δ(s,α)|≤1. These constraints should extend to the choice of the initial state as well: deterministic automata should have at most one initial state (that what we wrote), and complete automata should have at least one initial state. But somehow this last "initial" word is missing from our definition of complete.
I don't know how this word got missing, and why we didn't notice it before.
I remember we discussed these definition in Brno when we were writing the first draft, and that I had to dig up several papers to prove that these definitions are used.
In a complete automaton there always exists a way to read any letter letter α from any state s, so |δ(s,α)|≥1. In a deterministic automaton there is at most one way to do so: |δ(s,α)|≤1. These constraints should extend to the choice of the initial state as well: deterministic automata should have at most one initial state (that what we wrote), and complete automata should have at least one initial state. But somehow this last "initial" word is missing from our definition of
complete.