1. Program to DFA: Note in binary if x = 1012 = 5 and y = 10112 = 11 then y = 2 x + 1. Remember x mod 3 = 2 is the remainder when you divide x by 3. Consider the following program:

q = 0

loop until no more characters

get(c) % c {0, 1}

q = (2 q + c) mod 3 % q {0, 1, 2}

end loop

if q = 0 then return(accept)

else return(reject)

end if

(a) What language does this program accept?

(b) Convert the program into a DFA.