HM5-Chapters8-9 - CS 341 Automata Theory Elaine Rich...

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CS 341 Automata Theory Elaine Rich Homework 5 Due: Thursday, February 15, 2007 This assignment covers Chapters 8 and 9. 1) For each of the following languages L , state whether or not L is regular. Prove your answer: a) { a i b j : i, j ≥ 0 and i + j = 5}. b) { a i b j : i, j ≥ 0 and i - j = 5}. c) { w = xy : x , y { a , b }* and | x | = | y | and # a ( x ) # a ( y )}. d) { w = xyzy R x : x , y , z { a , b }*}. e) { w = xyzy : x , y , z { 0 , 1 } + }. f) { w {0, 1}* : # 0 ( w ) # 1 ( w )}. g) { w { a , b }* : 5 x { a , b } + ( w = x x R x )}. h) { w { a , b }* : the number of occurrences of the substring ab equals the number of occurrences of the substring ba }. i) { w : w { a z }* and the letters of w appear in reverse alphabetical order}. For example, spoonfeed L . j) L 0 *, where L 0 = { ba i b j a k , j 0, 0 i k }. 2) For each of the following languages L , state whether L is regular or not and prove your answer: a) { uww R v : u
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HM5-Chapters8-9 - CS 341 Automata Theory Elaine Rich...

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