Solution-Introduction+to+Automata+Theory

Solution-Introduction+to+Automata+Theory - SOLUTIONS...

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1 SOLUTIONS I ntroduction t o A utomata T heory, L anguages, a nd C omputation Collected & Prepared By rontdu@gmail.com 13 th Batch (06-07) Dept. of Computer Science & Engineering University of Dhaka Copyright: No copyright
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2 TABLE OF CONTENTS SOLUTIONS FOR CHAPTER 2 SOLUTIONS FOR SECTIONS: 2.2 . ............................................................ 4 SOLUTIONS FOR SECTIONS: 2.3 . ............................................................ 8 SOLUTIONS FOR SECTIONS: 2.4 . ............................................................ 9 SOLUTIONS FOR SECTIONS: 2.5 . ........................................................... 10 SOLUTIONS FOR CHAPTER 3 SOLUTIONS FOR SECTIONS: 3.1 . ........................................................... 11 SOLUTIONS FOR SECTIONS: 3.2 . ........................................................... 12 SOLUTIONS FOR SECTIONS: 3.4 . ........................................................... 13 SOLUTIONS FOR CHAPTER 4 SOLUTIONS FOR SECTIONS: 4.1 . ........................................................... 14 SOLUTIONS FOR SECTIONS: 4.2 . ........................................................... 15 SOLUTIONS FOR SECTIONS: 4.3 . ........................................................... 17 SOLUTIONS FOR SECTIONS: 4.4 . ........................................................... 18 SOLUTIONS FOR CHAPTER 5 SOLUTIONS FOR SECTIONS: 5.1 . ........................................................... 19 SOLUTIONS FOR SECTIONS: 5.2 . ........................................................... 20 SOLUTIONS FOR SECTIONS: 5.3 . ........................................................... 20 SOLUTIONS FOR SECTIONS: 5.4 . ........................................................... 20 SOLUTIONS FOR CHAPTER 6 SOLUTIONS FOR SECTIONS: 6.1 . ........................................................... 22 SOLUTIONS FOR SECTIONS: 6.2 . ........................................................... 22 SOLUTIONS FOR SECTIONS: 6.3 . ........................................................... 24 SOLUTIONS FOR SECTIONS: 6.4 . ........................................................... 25 SOLUTIONS FOR CHAPTER 7 SOLUTIONS FOR SECTIONS: 7.1 . ............................................................ 26 SOLUTIONS FOR SECTIONS: 7.2 . ............................................................ 28 SOLUTIONS FOR SECTIONS: 7.3 . ............................................................ 30 SOLUTIONS FOR SECTIONS: 7.4 . ............................................................ 32
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3 SOLUTIONS FOR CHAPTER 8 SOLUTIONS FOR SECTIONS: 8.1 . ............................................................ 34 SOLUTIONS FOR SECTIONS: 8.2 . ............................................................ 34 SOLUTIONS FOR SECTIONS: 8.3 . ............................................................ 36 SOLUTIONS FOR SECTIONS: 8.4 . ............................................................ 37 SOLUTIONS FOR SECTIONS: 8.5 . ............................................................ 38 SOLUTIONS FOR CHAPTER 9 SOLUTIONS FOR SECTIONS: 9.1 . ............................................................ 39 SOLUTIONS FOR SECTIONS: 9.2 . ............................................................ 39 SOLUTIONS FOR SECTIONS: 9.3 . ............................................................ 41 SOLUTIONS FOR SECTIONS: 9.4 . ............................................................ 43 SOLUTIONS FOR SECTIONS: 9.5 . ............................................................ 44 SOLUTIONS FOR CHAPTER 10 SOLUTIONS FOR SECTIONS: 10.1 . ........................................................... 45 SOLUTIONS FOR SECTIONS: 10.2 . ........................................................... 46 SOLUTIONS FOR SECTIONS: 10.3 . ........................................................... 46 SOLUTIONS FOR SECTIONS: 10.4 . ........................................................... 47 SOLUTIONS FOR CHAPTER 11 SOLUTIONS FOR SECTIONS: 11.1 . ........................................................... 50 SOLUTIONS FOR SECTIONS: 11.3 . ........................................................... 51 SOLUTIONS FOR SECTIONS: 11.5 . ........................................................... 52
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4 Introduction to Automata Theory, Languages, and Computation Solutions for Chapter 2 Revised 9/6/01. Solutions for Section 2.2 Exercise 2.2.1(a) States correspond to the eight combinations of switch positions, and also must indicate whether the previous roll came out at D , i.e., whether the previous input was accepted. Let 0 represent a position to the left (as in the diagram) and 1 a position to the right. Each state can be represented by a sequence of three 0's or 1's, representing the directions of the three switches, in order from left to right. We follow these three bits by either a indicating it is an accepting state or r , indicating rejection. Of the 16 possible states, it turns out that only 13 are accessible from the initial state, 000r. Here is the transition table: A B ->000r 100r 011r *000a 100r 011r 100r 010r 111r *100a 010r 111r
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5 Exercise 2.2.2 The statement to be proved is δ - hat(q,xy) = δ - hat(δ -hat(q,x),y) , and we proceed by induction on the length of y . Basis: If y = ε , then the statement is δ - hat(q,x) = δ - hat(δ - hat(q,x),ε) . This statement follows from the basis in the definition of δ -hat . Note that in applying this definition, we must treat δ -hat(q,x) as if it were just a state, say p . Then, the statement to be proved is p = δ - hat(p,ε) , which is easy to recognize as the basis in the definition of δ -hat .
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This note was uploaded on 03/23/2011 for the course CS 627 taught by Professor Friesen during the Spring '11 term at Texas A&M.

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Solution-Introduction+to+Automata+Theory - SOLUTIONS...

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