Discrete Math
State a b c Final? 1 3 — 2 x 2 4 x 3 3 5 x 4 6 ✓ 5 5 6 ✓ 6 1 ✓
Problem 2
Write regular expressions that match the following string patterns. Feel free to ask on Piazza whether example strings match the pattern or not, if you’re not sure. (a) All strings made of of as, bs, and cs, and ds that have only two different kinds of letters in them . The empty string counts. (b) All strings made up of as and bs that have an even number of letters .
Problem 3
(30 points) Draw NFAs that match the following regular expressions: (i) (10 points) ((ab)1(ba))* (ii) (10 points) (Pih)(ii0)(tIp) (iii) (10 points) e(Y1x)*Y”
Problem 4
Use the subset construction to build DFAs that correspond to the given NFAs. Write out your DFA tables by listing all of the NFA states that are part of the same DFA state, and whether something is final. For example:
(a) NFA 1:
State a b c Final?
1,2 2,4 — 1,4 x
y
