Question & Answer: For alphabet {x,y,z}, all strings that contain xyx or zyz…..

For alphabet {x,y,z}, all strings that contain xyx or zyz

(1) Write a regular expression for the language.

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(2) Define a finite state machine (FSM) that recognizes words in the language (input alphabet, states, start state, state transition table, and accept states). Include a state digraph for the FSM.

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Question & Answer: For alphabet {x,y,z}, all strings that contain xyx or zyz..... 1

1. The first two lines are the regular expression of the language. They are the same but the second one is the minified version of the first one. Here + means or operator(any one of those) and * means Kleen’s closure (a* means null or a or aa or aaa till infinite length strings). So in the beginning or the end could be any combinations of x, y or z but in there somewhere there must xyx or zyz. This would include all the strings irrespective of where zyz or xyx might be.

2. The input alphabets are x, y and z. There are 6 states as shown in the diagram. There starting state is the state 1 where as the final/accepting state is the state 6. The transition table is:

State x y z

1 2 1 4

2       2 3 4

3 6 1 4

4 2 5 4

5 2 1 6

6 6 6 6

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