# HM7-Grammars-ParseTrees-Ambiguity-Answers - CS 341 Automata...

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Unformatted text preview: CS 341 Automata Theory Elaine Rich Homework 7 Due: Thursday, March 1, 2007 This assignment covers Sections 11.1 - 11.6. 1) Let Σ = { a , b }. For the languages that are defined by each of the following grammars, do each of the following: i . List five strings that are in L . ii . List five strings that are not in L . iii . Describe L concisely. You can use regular expressions, expressions using variables (e.g., a n b n , or set theoretic expressions (e.g., { x : …}) iv . Indicate whether or not L is regular. Prove your answer. a) S → a S | S b | ε i. ε , a , b , aaabbbb , ab ii . ba , bbaa , bbbbba , ababab , aba iii . L = a * b * iv . L is regular because we can write a regular expression for it. b) S → a S a | b S b | a | b i. a , b , aaa , bbabb , aaaabaaaa ii . ε , ab , bbbbbbba , bb , bbbaaa iii . L is the set of odd length palindromes, i.e., L = { w = x ( a ∪ b ) x R , where x ∈ { a , b }*}. iv . L is not regular. Easy to prove with pumping. Let w = a k baba k . y must be in the initial a region....
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