Problem 1

a) Let the alphabet ={ 0,1 }. Write a regular expression for each of the following. In this question, you may not use the extended notation (only union, concatenation, and Kleene star).

Problem 1 a) Let the alphabet 10,1 h. Write a regular expression for each of the following. In this question, you may not use the extended notation (only union, concatenation, and Kleene star) i. Bit strings that have an even number of 0's ii. All words in which '1' appears tripled (and only tripled, meaning all 1's must appear in groups of three). The empty string is also accepted. Please note that blocks offour 1's should not be accepted here. iii. All bit strings that do not have substring '01'. iv. All bit strings that contain exactly two 0's or exactly three 0's. b) Write down all strings that are matched by the following regular expression (If there are infinitely many, clearly a pattern e. a, aa, aaa, (very) (chubby)? (shortlugly) (wo)?man c) Write a formal grammar forthe alphabet a,b,c )that accepts the language of strings that is read the same forward and backwards (i e. 'abcba' is in the language but "bcab' is not)