Computer Science 172 - Fall 1999 - Jordan - Midterm 1

Computer Science 172 - Fall 1999 - Jordan - Midterm 1 - CS...

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CS 172, Midterm, Fall 1999 CS 172, Fall 1999 Midterm Professor M. Jordan 172 students: On this exam, I am more interested in testing your ability in setting up the solution to a variety of problems than necessarily in getting all of the details. I don't expect anyone to answer all of the questions fully and correctly. We will be reasonably generous with partial credit, so it would be better to provide partial answers to many questions than complete answers to a few questions. For the more difficult questions, you might consider first writing down a brief section called "Sketch of answer," and later, if you have time, writing down a more detailed section called "Details." --Mike Problem #1 Closure properties of languages associated with Turing machines. (a) Prove that the union of two Turing-recognizable languages is Turing recognizable. (b) Prove that the union of two decidable languages is decidable. Problem #2 Show that the class of context-free languages is closed under *. ( Hint : It is probably easiest to do this with a grammer, where a fairly simple construction suffices, but it is doable with PDA's if you prefer).
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