CS381-2005fa-final - CS 381 Fall 2005 Final Exam Closed...

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CS 381 Final Exam Wednesday Dec 14 Fall 2005 Closed book Philips 101 7-9:30pm All problems should be straight forward. Partial credit will depend on clarity and conciseness of your answer. Please do not put down correct but irrelevant information. 1. Construct a finite automaton for the set of all strings of 0’s and 1’s with an even number of zeros and an odd number of ones. You can draw the state diagram of the finite automaton or you can specify the delta function by a table. In either case you must indicate the start state and the set of final states. 2. Give a one or two sentence definition of the symbol k ij R which was used in converting a finite automaton to a regular expression. 3. Let L= { } 2 |1 n n ab n . Prove or disprove that L is a context-free language. 4. Let L= { } nnn abc abc n +++ −≥ . Either give a context-free grammar for L or use the
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