CS381-2002fa-final - CS381 Fall 2002 Final Exam Thursday...

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CS381 Final Exam Thursday Dec 19, 2002 Fall 2002 Location Olin 155 12:00-2:30pm This is a 2 and ½ hour in class closed book exam. All questions are straightforward and you should have no trouble doing them. Please show all work and write legibly. Thank you. 1. Let * ) ( b a R + be a regular set. Consider the set consisting of all strings that can be obtained from strings in R by deleting two b’s. Is this set regular? Give rigorous proof of your answer. 2. Let * ) ( c b a R + + be a regular set. Rearrange the symbols in each string of R so that all a ’s appear first, then the b ’s and then the c ’s. a) Is the resulting set regular? b) Is it context free? 3. Prove or disprove that { } l j or k i either d c b a l k j i = = | is a context-free language. 4. Prove or disprove each of the following: a) The class of context-free languages is closed under intersection.
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