Finite state machines

Finite state machine (FSM) with output

Q, a set of states

S, a single state which is an element of Q. This is the start state.

Sigma, the input alphabet

Pi, the output alphabet

delta, a transition function that maps a state and a letter from the input alphabet,

to a state and a letter from the output alphabet

Primary differences with FSA:

No final state

Transition function generates output as well as determining next state

Purpose is not to recognize strings, but to generate set of outputs

Describes how inputs and current state generate outputs

For circuits:

Input alphabet: set of k-bit strings

Output alphabet: set of m-bit strings

Transitions from a given state must be:

Mutually exclusive: only 1 choice for any single input value

Exhaustive: all possible inputs have a transition

"Nothing happens": remain in same state