Talk:Discrete Mathematics/Finite state automata

Formality of the definition
I debate the formality of these definitions. I don't think they are strict enough. I think a better pair of definitions would be:

Formally, a Deterministc Finite Automaton is a 5-tuple $$D=(Q,\Sigma ,\delta ,s,F)$$ where:

$$Q$$ is the finite set of states. $$\Sigma$$ is the finite alphabet. $$\delta :Q\times \Sigma \rightarrow Q$$ is the transition function. $$s$$ is the starting state. $$F\subseteq Q$$ is the set of accepting states.

Similarly, the formal definition of a Nondeterministic Finite Automaton is a 5-tuple $$N=(Q,\Sigma ,\delta ,s,F)$$ where:

$$Q$$ is the set of all states. $$\Sigma$$ is the finite alphabet. $$\delta :(Q\cup \{ \epsilon \} )\times \Sigma \rightarrow \mathcal{P}(Q)$$ is the transition function. Note that for some set $$S,\mathcal{P}(S)=\{ X\subseteq S\}$$. $$s$$ is the starting state. $$F\subseteq Q$$ is the set of accepting states.

and if the transition functions are not clear enough, give example usage eg for a DFA, $$\delta (q_0,a)=q$$ for some $$q_0,q\in Q,a\in \Sigma$$ and for an NFA, $$q\in \delta (q_0,a)$$

Beast257 (talk) 17:25, 13 June 2010 (UTC)