Reference no: EM13928901
1. Consider the deterministic finite automaton M = ({q1, q2, q3}, {0, 1}, ∂, q1, {q2}) where is dened as follows:
- (q1, 0) = q1
- (q1, 1) = q2
- (q2, 0) = q3
- (q2, 1) = q2
- (q3, 0) = q2
- (q3, 1) = q2
Write an equivalent regular expression.
2. Prove that the following languages are not regular sets:
(a) L = faibjck j i = 0 _ j = k, i; j; k 0g. Example strings include bccc, abbcc, aaa, etc.
(b) L = fww j w 2 f0; 1g+g. Example strings include 00, 11, 0101, 010010, etc.
(c) L = fa2n j n 0g. Example strings include aaaa, a16, a64, etc.
(d) L = fw j w 2 f0; 1g, w is of the form (0i1)n, for i = 1, 2, ..., n, n 0g. The strings of this language are ", 01, 01001, 010010001, ...., each successive string of 0's being one larger than the previous.
3. Find the minimum state nite automaton for the language specied by the nite automaton M = (fq0, q1, q2, q3g, f0, 1g, , q0, fq0g) where is dened as follows:
- (q0, 0) = q3
- (q0, 1) = q0
- (q1, 0) = q0
- (q1, 1) = q3
- (q2, 0) = q2
- (q2, 1) = q1
- (q3, 0) = q1
- (q3, 1) = q2
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