Download presentation

Presentation is loading. Please wait.

Published bySpencer Nunley Modified over 2 years ago

1
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b List all unordered pairs of distinct states (p, q). Make a sequence of passes through these pairs as follows. On the first pass, mark each pair (p, q) for which exactly one of the two states p and q is in A. On each subsequent pass, examine each unmarked pair (r, s); if there is a symbol σ ∈ such that δ(r, σ) = p, δ(s, σ) = q, and the pair (p, q) has already been marked, then mark (r, s). After a pass in which no new pairs are marked, stop. At that point, the marked pairs (p, q) are precisely those for which p q.

2
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b 1 Pair (2, 1) is marked on the first pass because 2 is an accepting state and 1 is not.

3
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b 1 Pair (6, 1) is marked on the first pass because 6 is an accepting state and 1 is not. 1

4
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b Pair (3, 2) is marked on the first pass because 2 is an accepting state and 3 is not. 1 1 1

5
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b Pair (4, 2) is marked on the first pass because 2 is an accepting state and 4 is not. 1 1 1 1

6
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b Pair (5, 2) is marked on the first pass because 2 is an accepting state and 5 is not. 1 1 1 1 1

7
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b Pair (7, 2) is marked on the first pass because 2 is an accepting state and 7 is not. 1 1 1 1 1 1

8
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b Pair (6, 3) is marked on the first pass because 6 is an accepting state and 3 is not. 1 1 1 1 1 1 1

9
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b Pair (6, 4) is marked on the first pass because 6 is an accepting state and 4 is not. 1 1 1 1 1 1 1 1

10
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b Pair (6, 5) is marked on the first pass because 6 is an accepting state and 5 is not. 1 1 1 1 1 1 11 1

11
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b Pair (7, 6) is marked on the first pass because 6 is an accepting state and 7 is not. 1 1 1 1 1 1 11 1 1

12
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b Pair (4, 1) is marked on the second pass because δ(4, a) = 4 and δ(1, a) = 2. (4, 2) was marked in pass one. 2 1 1 1 1 1 1 111 1 a a

13
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b 1 2 1 1 1 1 1 111 1 2 Pair (4, 3) is marked on the second pass because δ(4, a) = 4 and δ(3, a) = 6. (6, 4) was marked in pass one. a a

14
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b 1 2 1 1 1 1 1 2 1 2 11 1 Pair (5, 4) is marked on the second pass because δ(5, a) = 6 and δ(4, a) = 4. (6, 4) was marked in pass one. a a

15
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b 1 2 1 1 1 1 1 2 1 2 1 2 1 1 Pair (7, 4) is marked on the second pass because δ(7, a) = 6 and δ(4, a) = 4. (6, 4) was marked in pass one. a a

16
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b 1 2 1 1 1 1 1 2 1 2 1 2 1 1 Using the above information we can now determine the states in the minimum-state FA.

17
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b 1 2 1 1 1 1 1 2 1 2 1 2 1 1 We will combine states 1, 3, 5, and 7.

18
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b 1 2 1 1 1 1 1 2 1 2 1 2 1 1 We will also combine states 6 and 2.

19
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b 1 2 1 1 1 1 1 2 1 2 1 2 1 1 State 4 will be a new state. 212

20
Find a minimum-state FA recognizing the same language as the given FA. 1 3 7 2 5 4 6 b b a a a a a a a b b b b 123456 2 3 4 5 6 7 b 1 2 1 1 1 1 1 2 1 2 1 2 1 1 Below is our minimum-state FA as outlined before: 1,3, 5, 7 6,2 4 b b b a a a

Similar presentations

OK

Chapter 3 Regular Expressions, Nondeterminism, and Kleene’s Theorem Copyright © 2011 The McGraw-Hill Companies, Inc. Permission required for reproduction.

Chapter 3 Regular Expressions, Nondeterminism, and Kleene’s Theorem Copyright © 2011 The McGraw-Hill Companies, Inc. Permission required for reproduction.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Download ppt on fundamental rights and duties of a citizen Ppt on water our lifeline Elementary ppt on main idea Ppt on centring sheet Ppt on windows vista operating system Ppt on soft skills download Ppt on kingdom monera facts Ppt on earth and space book Pdf to ppt online converter Ppt on speed control of dc motor using pwm