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2. Consider the regular expression:

(ab | ac)

a. Use Thompsons construction to construct an NFA.

b. Convert the NFA to DFA using subset construction.

c. Minimize the DFA

3. One way of proving that two REs are equivalent is to construct their minimized DFA and then compare them. If they differ only by state names, then the REs are equivalent. Use this technique to check the following pairs of REs and state whether or not they are equivalent.

a. (0 | 1) and (0 | 10 )

1. Write a regular expression for each of the following languages:

(a) Given an alphabet = {0, 1}, L is the set of all strings of alternating pairs of 0s and pairs of 1s.

(b) Given an alphabet = {0, 1}, L is the set of all strings thatcontain an even number of 0s or an even number of 1s.

(c) Given an alphabet = {a, b, c, d}, L is the set of all strings in which the letters appear in strictly ascending lexicographical order. Strictly ascending means that the same letter cant appear twice.