Deterministic Finite Automata

[jnthn]

Can the alphabet of a DFA be a set of math operations? For example, \(\displaystyle \Sigma\) = {-1, +0, +1}.

 

[daon]

Its been awhile since I've studied automata, but a DFA's alphabet can be anything you want it to be. You can define the accept states, for example: {w | evaluating w gives an even number}.

It will have 3 nodes, start, odd, even. The full DFA can be drawn as:


q->+0,+1,-1
n->n+0=n, n+1, n-1

 

[jnthn]

Thanks! I wasn't entirely sure if the following DFA was kosher or not, but now I know. The state with the "1" in it is the start state, the black state is the reject state, and the red and blue are accept states (red = even, blue=odd)