Can you please help me with this problem and the sections that come along with this problem because I am struggling big time with this. I need help with section 1.10 part A but you will need exercise 1.6b to answer the questions for 1.10 part A. I have attached both exercises below and you will need the theorm which I have provided as well. Can you please draw the state diagram and do something visual so I ca understand it better. question for 1.10: 1.10 Use the construction in the proof of Theorem 1.49 to give the state diagrams of NFAs recognizing the star of the languages described in a. Exercise 1.6b Exercise 1.6b: 1.6 Give state diagrams of DFAs recognizing the following languages. In all parts, the alphabet is {0,1}. b) {w| w contains at least three 1s}
Can you please help me with this problem and the sections that come along with this problem because I am struggling big time with this. I need help with section 1.10 part A but you will need exercise 1.6b to answer the questions for 1.10 part A. I have attached both exercises below and you will need the theorm which I have provided as well. Can you please draw the state diagram and do something visual so I ca understand it better.
question for 1.10:
1.10 Use the construction in the proof of Theorem 1.49 to give the state diagrams of NFAs recognizing the star of the languages described in
a. Exercise 1.6b
Exercise 1.6b:
1.6 Give state diagrams of DFAs recognizing the following languages. In all parts, the alphabet is {0,1}.
b) {w| w contains at least three 1s}
 alt="THEOREM
1.49
The class of regular languages is closed under the star operation.
PROOF IDEA We have a regular language A₁ and want to prove that A₁ also
is regular. We take an NFA N₁ for A₁ and modify it to recognize At, as shown in
the following figure. The resulting NFA N will accept its input whenever it can
be broken into several pieces and N₁ accepts each piece.
We can construct N like N₁ with additional e arrows returning to the start
state from the accept states. This way, when processing gets to the end of a piece
that N₁ accepts, the machine N has the option of jumping back to the start state
to try to read another piece that N₁ accepts. In addition, we must modify N
so that it accepts e, which always is a member of A. One (slightly bad) idea is
simply to add the start state to the set of accept states. This approach certainly
adds e to the recognized language, but it may also add other, undesired strings.
Exercise 1.15 asks for an example of the failure of this idea. The way to fix it is
to add a new start state, which also is an accept state, and which has an e arrow
to the old start state. This solution has the desired effect of addinge to the
language without adding anything else.
N₁
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