Here is the transition table of a DFA that we shall call M: 0 1 →A B G B C H C D G D A H E F C F G I G H C H A D I E I Find the minimum-state DFA equivalent to the above. States in the minimum-state DFA are each the merger of some of the states of M. Find in the list below a set of states of M that forms one state of the minimum-state DFA. a) {B} b) {A,B} c) {C,H} d) {C,D} 3. Design the minimum-state DFA that accepts all and only the strings of 0's and 1's that have 110 as a substring. To verify that you have designed the correct automaton, we will ask you to identify the true statement in a list of choices. These choices will involve: The number of loops (transitions from a state to itself). The number of transitions into a state (including loops) on input 1. The number of transitions into a state (including loops) on input 0. Count the number of transitions into each of your states ("in-transitions") on input 1 and also on input 0. Count the number of loops on input 1 and on input 0. Then, find the true statement in the following list. a) There is one state that has two in-transitions on input 0. b) There is one state that has one in-transition on input 0. c) There are two states that have one in-transition on input 0. d) There are two loops on input 0 and two loops on input 1. 4. Here is the transition table of a DFA: 0 1 →A E D B A C C G B D E A E H C F C B G F E H B H Find the minimum-state DFA equivalent to the above. Then, identify in the list below the pair of equivalent states (states that get merged in the minimization process). a) E and G b) C and D c) A and B d) F and G

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.7: Cooridinates And Change Of Basis

Problem 58E

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Question

Here is the transition table of a DFA that we shall call M:

	0	1
→A	B	G
B	C	H
*C	D	G
*D	A	H
E	F	C
F	G	I
*G	H	C
*H	A	D
I	E	I

Find the minimum-state DFA equivalent to the above. States in the minimum-state DFA are each the merger of some of the states of M. Find in the list below a set of states of M that forms one state of the minimum-state DFA.

{B}

{A,B}

{C,H}

{C,D}

Design the minimum-state DFA that accepts all and only the strings of 0's and 1's that have 110 as a substring. To verify that you have designed the correct automaton, we will ask you to identify the true statement in a list of choices. These choices will involve:

The number of loops (transitions from a state to itself).
The number of transitions into a state (including loops) on input 1.
The number of transitions into a state (including loops) on input 0.

Count the number of transitions into each of your states ("in-transitions") on input 1 and also on input 0. Count the number of loops on input 1 and on input 0. Then, find the true statement in the following list.

		a)	There is one state that has two in-transitions on input 0.
		b)	There is one state that has one in-transition on input 0.
		c)	There are two states that have one in-transition on input 0.
		d)	There are two loops on input 0 and two loops on input 1.

Here is the transition table of a DFA:

	0	1
→A	E	D
*B	A	C
C	G	B
D	E	A
*E	H	C
F	C	B
G	F	E
H	B	H

Find the minimum-state DFA equivalent to the above. Then, identify in the list below the pair of equivalent states (states that get merged in the minimization process).

E and G

C and D

A and B

F and G

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