FAO Comp Sci students/people

[Greenlizard0]

Allo, am running through my notes on Automata theory and languages. I'm unsure of a few things, possibly because more than one answer is possible.

Q)Consider the language that consists of all words over the alphabet {a,b,c}, that either begin with the letter a, or begin with b and contain exactly three c's.

a) draw a diagram of a deterministic finite automaton that accepts the language
b) Write a regular expression for the language, and explain briefly how our regular expression corresponds with the language

I get :

States 1,2,3,4,5,6. States 1 to 2 with an arrow labelled a. States 1 to 3 with an arrow labelled b. States 3,4,5,6 loop themselves with an arrow each, labelled a,b. States 1 to 3, 3 to 4, 4 to 5 and 5 to 6 have arrows with c above them. State 5 is an accepting state.

How do I pull out a regular expression for part b) ? I understand that an RE uses U, concat and Keene*.

Similarly for this question, how do I get a regular expression please?

Q)Consider the following NFA A=(Q,A,PHI,i,T) where :

alphabet A ={a,b}
states Q={i,r,s,t}
accepting states T={s,t}
transition function PHI is :

PHI(i,a)=r PHI(r,b)=s PHI(s,a)={r,t} PHI(t,b)=t

Again, the question asks to create a regular expression.

Any help would be appreciated, preferably in prose rather than formally please.