Finite state machines

Combinational circuit: implements Boolean function

Sequential circuit: implements finite state machine

May also contain combinational circuit

In programming languages (i.e., 330), DFA (deterministic finite automaton)

Essentially the same, but different purpose

DFA:

Q, a set of states

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

F, a set of states designated as the final states

Sigma, the input alphabet

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

to the next state

DFA is used to recognize a language L, which is composed of a set of strings

made up from an input alphabet

If DFA can recognize strings in the language, then L has a regular grammar

To use DFA:

Start in initial state S

Process each character in the input string, moving from state to state

If DFA in a final state after processing the last character, string in language

Example: alphabet a, b

Is string "aabb" recognized by a DFA?