Find L_4. Show that L_k is finite. Let A = {a, b, c}. Describe the language L_r

Question

Find L_4. Show that L_k is finite. Let A = {a, b, c}. Describe the language L_r for each regular expression: r = ab*c* r = a* b*c* Let A = {a, b}. Find a regular expression r such that the language L_r consists of all words w where: w begins with a^2 and ends with b^2 w contains an even number of a's Consider the grammar S rightarrow aS |aSbS| epsilon This grammar is ambiguous. Show in particular that the string aab has two: Parse trees Leftmost derivations Rightmost derivations Find an unambiguous grammar for this language

Explanation / Answer

Question 3:

a) Every string in the expression will be of the form ab^xc^y where x and y are non-negative integers. So every string starts with only one 'a' and then we have zero or more b's and followed 0 or more c's.

b) There are two possibilities for every string in the expression. The first on is that it will either have zero or more a's. The second possibility is that it will have zero or more b's and followed 0 or more c's.

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