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Theory of Automata CS402

Q1. Show that the following pairs of regular expressions define the same language over the alphabet

L = {a, b}.

(i) (ab)*a         and    a(ba)*

(ii) (a* + b)*    and    (a + b)*

(iii) (a* + b*)* and    (a + b)*

[9 marks = 3*3]

Q2. Develop a regular expression for the following language over the alphabet P = {a, b} such that it accepts all strings in which the letter b is never tripled. This means that no word contains the substring bbb.                                                                                                                                          [5 marks]

Q3. Develop a regular expression for the following language over the alphabet P = {a, b} such that it accepts all strings all words in which a is tripled or b is tripled, but not both. This means each word contains the substring aaa or the substring bbb but not both.                                                 [ 6 marks]

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