Hw5 - Homework 5  CISC 303 Timo Kötzing (tkoe@udel.edu)...

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Unformatted text preview: Homework 5  CISC 303 Timo Kötzing (tkoe@udel.edu) Handed out: Monday, March 16. Due Date: Friday, March 27. Problem 1. (2 points) (i) What is the singular of automata? (ii) Describe, in your own words, rst the syntactic, then the semantic dierence of the words complement and compliment. Problem 2. (12 points) Give three PDAs (i) (ii) (iii) in graphical notation only L0 = {w ∈ A∗ | w = wR } accepting L0 , L1 and L2 as dened just below, respectively. is the set palindromes (words that read the same forwards as backwards). L1 = {an bk c2n | n, k ≥ 1}. L2 is the set of all strings from the alphabet containing all and only the symbols [,],{},(,) such that all parenthesis match with their type. Hence, [()[{}]] ∈ L2 , but [[)] ∈ L2 and [{(∈ L2 . Problem 3. (4 points) Give a DPDAs in graphical notation only accepting L3 as dened just below. L3 = {w · c · wR | w ∈ {a, b}∗ }. Problem 4. (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}∗ }. z as given u, v, w, x, y can Hint: For how your by Pumping for CFLs, pump the string r = az bz az bz . Distinguish many possible cases for look like. Problem 5. (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. Give an algorithm that takes two PDAs M0 and M1 and return a PDA M such that L(M ) = L(M0 ) · L(M1 ). Careful: Don't forget that each PDA expects a $ at the end of a word, and that each PDA expects an empty stack at the beginning of the computation. Show the result of your algorithm applied to the PDAs from 2.1.2 and 2.1.3 from the Lecture Notes. You don't need to give the algorithm in full set-theoretic detail 1 ...
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