Hw5Mathy - Homework 5 Mathy Version CISC 303 Timo...

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Unformatted text preview: Homework 5 Mathy Version CISC 303 Timo Kötzing ([email protected]) Handed out: Monday, March 16. Due Date: Friday, March 27. Problem 1. (8 points) (i) Give a PDAs in graphical notation only accepting L as de ned just below. L is the set of all strings from the alphabet containing all and only the symbols [,],{},(,) such that all parenthesis match with their type. Hence, [()[ {} ]] ∈ L 1 , but [[)] 6∈ L 1 and [ { ( 6∈ L 1 . (ii) Give a DPDA in graphical notation only accepting L 1 as de ned just below. L 1 = { w cot c · w R | w ∈ { a,b } * } . Problem 2. (8 points) This is a group problem . Work on this problem in a group of no more than ve people. Each of you has to submit the solution for this problem, clearly indicating who you worked with. Use Pumping for CFLs to show that the following language L is not a CFL. L = { ww | w ∈ { a,b } * } . Problem 3. (8 points) A Monoid is a pair ( M, · ) such that M is a set and M is an operation on M , i.e., · : M × M → M such that ∀...
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