Download presentation

1
**DFA vs NFA Deterministic Finite Automata**

Non-Deterministic Finite Automata Characterized as 5-tuple < S, A, T, s0, F > S is the set of states A is the alphabet T is the transition function: S x A S s0 is the start state F is the set of accepting states. Characterized as 5-tuple < S, A, T, s0, F > S is the set of states A is the alphabet T is the transition function: S x (A{}) PS s0 is the start state F is the set of accepting states. Waseem Besada

2
**From NFA To DFA 1 Transition function for NFA b a 2 T a b **

{1} ø {3} a ø {2} ø ø ø ø {3} ø {4} 4 3 a {2} ø ø Waseem Besada

3
**Calculating The Transition function for DFA**

Transition function for NFA Transition function for DFA T a b T a b {1} ø {3} {0,3,4} ? ? ø {2} ø TD({0,3,4},a) = ({0},a) ({3},a) ({4},a) = {1,3} {3,4} {2} = {1,2,3,4} ø ø ø {3} ø {4} TD({0,3,4},b) = ({0},b) ({3},b) ({4},b) = ø ø ø = ø {2} ø ø Waseem Besada

4
**Calculating The Transition function for DFA (forts)**

Transition function for NFA T a b T a b {0,3,4} {1,2,3,4} ø {1} ø {3} ø ? ? ø ø ø {2} ø {1,2,3,4} ? ? {2,3,4} {2} ø ø ø {3} ø {4} TD({1,2,3,4},a) = ({1},a) ({2},a) ({3},a) ({2},a) = ø ø {3,4} {2} = {2,3,4} Similarly, TD({1,2,3,4},b) = {2} {2} ø ø Waseem Besada

5
**Calculating The Transition function for DFA (forts)**

Transition function for NFA T a b T a b {0,3,4} {1,2,3,4} ø {1} ø {3} ø ø ø ø {2} ø {1,2,3,4} {2,3,4} {2} ø ø ø {2,3,4} {2,3,4} {2} {3} ø {4} {2} ø ø {2} ø ø Waseem Besada

6
**Finally 1 2 3 4 Transition function for DFA T a b ø ? ? ø ø b 4 b a,b**

1 2 3 4 {0,3,4} {1,2,3,4} ø 2 1 ø ? ? ø ø a b {1,2,3,4} {2,3,4} {2} 3 {2,3,4} {2,3,4} {2} a {2} ø ø Waseem Besada

7
Exercise 2, solution 2. Construct directly (that is don’t use the transformation procedure given in the lecture) a DFA for each of the following REs. a) a | b b) a | b* c) ab* | bc* b a a,b a,b a a,c a,b,c b a,b a a,b b a,b a,b c a) b c c) a b) b Waseem Besada

8
Exercise 4, solution 4. Construct directly (that is don’t use the transformation procedure given in the lecture) a NFA for each of the following REs. a) a*bc*| bc b) a* | ab a c a b a c a b b) a) Waseem Besada

9
Exercise 5 5. Construct a DFA table for the following NFA transition table The start state is 0 and there is one accepting state, 2. a b 0 Ø {1,2} {1} {2} Ø Ø 2 Ø {2} {1} b 1 a b 2 b Waseem Besada

10
**Solution to exercise 5 DFA transition table NFA transition table T a b**

0 Ø {1,2} {1} {2} Ø Ø 2 Ø {2} {1} {0,1} ? ? {1,2} {1,2} {1,2} {1,2} {1,2} 1 a,b a,b 1 Waseem Besada

11
**Exercise 6 6. Consider the following NFA over the alphabet {a,b}:**

a) Find a regular expression for the language accepted by the NFA. b) Write down the transition table for the NFA. c) Transform the NFA into a DFA d) Draw a picture of the resulting DFA. a b a Waseem Besada

12
**Solution to exercise 6 (cont’d)**

Transition table for NFA T a b 0 {1} Ø {1,2} 1 Ø {2} Ø 2 {2} Ø Ø a b 1 2 a Waseem Besada

13
**Solution to exercise 6 (cont’d)**

Transition table for NFA Transition table for DFA T a b {0,1,2} {1,2} {2} {1,2} {2} {2} {2} {2} Ø Ø Ø Ø T a b 0 {1} Ø {1,2} 1 Ø {2} Ø 2 {2} Ø Ø Waseem Besada

14
**Solution to exercise 6(cont’d)**

{0,1,2} a Transition table for DFA {1,2} T a b {0,1,2} {1,2} {2} {1,2} {2} {2} {2} {2} Ø Ø Ø Ø b a,b {2} a Waseem Besada

15
Exercise 7 7. Transform each of the following REs into a NFA, then into a DFA a) a*b* b) a* | b* c) (a|b)* Solution to a) a b a 2 3 1 6 6 1 b 4 5 Waseem Besada

16
**Solution, exercise 6-a T a b Can be reduced to:**

{0,1,2,3} {1,2,3} {2,3} {1,2,3} {1,2,3} {2,3} {2,3} Ø {2,3} Ø Ø Ø a b 1 2 3 a a Can be reduced to: a a,b 1 b a b a,b 2 3 b a 2 3 b b Waseem Besada

17
**It is your turn to solve the rest of the exercises**

What to do next? It is your turn to solve the rest of the exercises Waseem Besada

Similar presentations

OK

Lecture 3UofH - COSC 3340 - Dr. Verma 1 COSC 3340: Introduction to Theory of Computation University of Houston Dr. Verma Lecture 3.

Lecture 3UofH - COSC 3340 - Dr. Verma 1 COSC 3340: Introduction to Theory of Computation University of Houston Dr. Verma Lecture 3.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on pierre simon laplace Ppt on three allotropes of carbon Ppt on varactor diode applications Ppt on earthquakes in india Ppt on success and failure quotes Ppt on aerobics oz Ppt on water softening techniques for managing Ppt on enterprise resource planning Ppt on organisational structure Download ppt on ceramic disc brake