cs373 fa10 hw9 - not provide a short informal...

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Problem Set 9 CS 373: Theory of Computation Assigned: November 9, 2010 Due on: November 16, 2010 at 10am Instructions: This homework has two parts. The first part has practice problems from the textbook many of whose solutions can be found in the textbook itself; you must not turn in solutions for these. The second part has 3 problems that can be solved in groups of size at most 3. Please strictly follow the homework guidelines given on the class website; submitions not following these guidelines will not be graded. Recommended Reading: Lectures 18, 19, 20 and pages 99 to 106, and Chapter 5 of class textbook. Practice Problems Solve problems 2.3, 2.4 (a) and (d), 2.6(a) and (c). Homework Problems Problem 1 . [Category: Comprehension] Consider the following grammar over the terminals { 0 , # } and start symbol S . S TT | U T 0 T | T 0 | # U 0 U 00 | # 1. For each of the following strings, answer whether or not they belong to the language defined by the grammar: 00#0#00, 0#0, 000#000000. If they do, give a derivation and parse tree for the string. If
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Unformatted text preview: not, provide a short, informal justification for why the string cannot be generated. [6 points] 2. What is the language of the grammar? You need not prove your answer, but you should provide a short informal justification for your answer. [2 points] 3. Is the language of the grammar regular? Prove your answer. [2 points] Problem 2 . [Category: Design+Proof] Design a context-free grammar for the language L = { a i b j | 2 i ≤ j ≤ 3 i, i,j ∈ N } . Provide a formal proof that your construction is correct. Hint: Build a grammar for the case when j = 2 i and j = 3 i , and think of a way to fuse the two together. [10 points] Problem 3 . [Category: Comprehension+Design+Proof] 1. Solve problem 2.27. [5 points] 2. Read about Post’s Correspondence Problem from section 5.2. Solve problem 5.21. [5 points] 1...
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