Dragon Book Exercise Answers Ch03 3.6 3.6

12/2 12/21/ 1/13 13

dragon dragon-bo -book ok-exercis -exercise-a e-ans nsw wers/ch ers/ch03 03/3 /3.6 .6/3 /3.6 .6.m .md d at maste asterr · fool2 fool2fish fish/d /dragon ragon-bo -book ok-exercis -exercise-a e-ans nsw wers · GitHub GitHub

 IC



Search or type a command

This repository



Explo xplore re

Featur Feat ures es

Ent nterp erpris rise e

Blog Bl og

    Star 

fool2fish / fool2fish  / Dragon-book-exercise-answers

 

master 

Sign up

  Dragon-book-exercise-answers / Dragon-book-exercise-answers / ch03 ch03 /  / 3.6 3.6 /  / 3.6.md

105

Sign in

   Fork

57

 

fool2fish 8 fool2fish 8 months ago update 3.6.1

 1  Co  Contributor  ntributor 

 

File

188 lines (158 sloc)

3.094 KB



Ope n

Ra w

Bl a m e

Hi story



3.6 Exercise

 

3.6.1! 3.4 Figure 3-19 exercises to calculate the failure function KMP algorithm. Illustrated in the case of a known failure function, and how according to the known keywords b_1b_2 ... b_n construct a DFA n +1 states  wit  with h the DFA can identify the language. * B_1b_2 ... b _n. Closer prove prove construct construct the DFA's time time complexity complexity is is O (n).

Answer  For illustration, a string abbaabb 3.4.3-3 example, failure function is: n: 1, 2, 3, 4, 5, 6, 7 f (n): 0, 0, 0, 1, 1, 2, 3 DFA was constructed as follows:

The DFA constructed pseudo-code:

for (i = 0; i
Obviously, in a known f (n) of the case, the time complexity of the algorithm is O (n)

https://g itithub.com/fool 2fi sh/dr ag on on- book- exer ci se- answer s/bl ob/master /ch03/3.6/3.6.md

1/3

12/21/13

dragon-book-exercise-answers/ch03/3.6/3.6.md at master · fool2fish/dragon-book-exercise-answers · GitHub

3.6.2 3.3.5 for the exercis e of each language to design a DFA or NFA.

3.6.3 NFA shown in Figure 3-29 to identify all labeled aabb path. The NFA accepts aabb it?

Answer  (0)-a-> (1)-a-> (2)-b-> (2)-b-> ((3)) (0)-a-> (0)-a-> (0)-b-> (0)-b-> (0) (0)-a-> (0)-a-> (1)-b-> (1)-b-> (1) (0)-a-> (1)-a-> (1)-b-> (1)-b-> (1) (0)-a-> (1)-a-> (2)-b-> (2)-b-> (2) (0)-a-> (1)-a-> (2)-b-> (2)-ε-> (0)-b-> (0) (0)-a-> (1)-a-> (2)-ε-> (0)-b-> (0)-b-> (0) The NFA apparently accepted aabb

3.6.4 For the NFA Figure 3-30, repeat the exercise 3.6.3

3.6.5 In practice is given below of the NFA conversion table: 1. Exercise 3.6.3 2. Exercise 3.6.4 3. Figure 3-26

Answer  Table 1 Status

a

b

ε

0

{0,1}

{0}

∅

1

{1,2}

{1}

∅

2

{2}

{2,3}

{0}

3

∅

∅

∅

Table 2 Status

a

b

ε

0

{1}

∅

{3}

1

∅

{2}

{0}

2

∅

{3}

{1}

3

{0}

∅

{2}

https://g ithub.com/fool2fish/drag on-book-exercise-answers/blob/master/ch03/3.6/3.6.md

2/3

12/21/13

dragon-book-exercise-answers/ch03/3.6/3.6.md at master · fool2fish/dragon-book-exercise-answers · GitHub

Table 3 Status

a

b

ε

0

∅

∅

{1,2}

1

{2}

∅

∅

2

{2}

∅

∅

3

∅

{4}

∅

4

∅

{4}

∅

© 2013 GitHub , Inc..

Terms

Privacy Security

Contact



https://g ithub.com/fool2fish/drag on-book-exercise-answers/blob/master/ch03/3.6/3.6.md

Status  API

Training

Shop

Blog  About

3/3