1. Construct or design a finite automaton give both a diagram and a formal definition (i.e. (Q,\Sigma,\delta, q0,F) -- express \delta as a table).

a) Design a Finite Automaton that accepts strings over the set {a,b} such that the length of the string is a multiple of 3.

b) Design a nite automaton that accepts all strings in the alphabet {a,b} where every occurrence of an a is followed by a b.