Question

3. (15 pt.) Prove that the class of regular languages is closed under intersection. That is,...

3. (15 pt.) Prove that the class of regular languages is closed under intersection. That is, show that if ? and ? are regular languages, then ? ∩ ? = {? | ? ∈ ? ??? ? ∈ ?} is also regular. Hint: given a DFA ?1 = (?1 , Σ, ?1 , ?1 , ?1) that recognizes ? and a DFA ?2 = (?2 , Σ, ?2 , ?2 , ?2) that recognizes ?, construct a new DFA ? = (?, Σ, ?, ?0 , ?) that recognizes ? ∩ ? and justify why your construction is correct.

Engineering   Computer-Science   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1


***Please give a like if you are satisfied with the answer. if you have any doubts or you need any further information ask me through comments. THANK YOU!***

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove that regular languages are closed under the set dierence operation. That is, if A and...
Prove that regular languages are closed under the set dierence operation. That is, if A and B are regular languages, then, A - B is also a regular language.
Each of the following languages is the union or intersection of two simpler languages. In each...
Each of the following languages is the union or intersection of two simpler languages. In each part, construct DFAs for the simpler languages, then combine them using the construction discussed in class to give the state diagram of a DFA for the language given. In all parts, Σ = {0,1}. 1. {w|w starts with an 0 and has at most one 1}
Draw the state diagram of DFAs recognizing the following languages. a. A = {w|w starts with...
Draw the state diagram of DFAs recognizing the following languages. a. A = {w|w starts with 0 and has odd length, or starts with 1 and has even length} b. B = {w|w is any string except 11 and 111} c. C = {, 0} Example of set difference: A = {0, 01}, and B = {0, 11}. Then, A − B = {01}. Prove that regular languages are closed under the set difference operation. That is, if A and...
Let swap_every_two be an operation on languages that is defined as follows: swap_every_two(L) = {a2a1a4a3 ....
Let swap_every_two be an operation on languages that is defined as follows: swap_every_two(L) = {a2a1a4a3 . . . a2na2n−1 | a1a2a3a4 . . . a2n−1a2n ∈ L where a1, . . . , a2n ∈ Σ} In this definition, Σ is the alphabet for the language L. 1. What languages result from applying swap every two to the following languages: (a) {1 n | n ≥ 0}, where the alphabet is {1}. (b) {(01)n | n ≥ 0}, where the...
Provide direct answers. This question has been posted here by someone else before, but the answer...
Provide direct answers. This question has been posted here by someone else before, but the answer is unreadable and does not indicate clearly the answer. DO C. Let Lodd = {w ∈ {0, 1}∗ | w contains an odd number of 0s}. a) - What is L∗odd? (arrive at a direct description of this language that does not refer to Lodd). b) Then Start with a DFA recognizing Lodd, and use the construction we saw in class to obtain an...
Provide direct answers. This question has been posted here by someone else before, but the answer...
Provide direct answers. This question has been posted here by someone else before, but the answer is unreadable and does not indicate clearly the answer. DO A. Let Lodd = {w ∈ {0, 1}∗ | w contains an odd number of 0s}. a) - What is L∗odd? (arrive at a direct description of this language that does not refer to Lodd). b) Then Start with a DFA recognizing Lodd, and use the construction we saw in class to obtain an...
Complete the proof Let V be a nontrivial vector space which has a spanning set {xi}...
Complete the proof Let V be a nontrivial vector space which has a spanning set {xi} ki=1. Then there is a subset of {xi} ki=1 which is a basis for V. Proof. We will divide the set {xi} ki=1 into two sets, which we will call good and bad. If x1 ≠ 0, then we label x1 as good and if it is zero, we label it as bad. For each i ≥ 2, if xi ∉ span{x1, . ....
BIOS 376 Homework 7 1. A professor claims that the mean IQ for college students is...
BIOS 376 Homework 7 1. A professor claims that the mean IQ for college students is 92. He collects a random sample of 85 college students to test this claim and the mean IQ from the sample is 84. (a) What are the null and alternative hypotheses to test the initial claim? (1 pt) (b) Using R, compute the test statistic. Assume the population standard deviation of IQ scores for college students is 17.6 points. (1 pt) (c) Using R,...
3.When closing entries are made:Immersive Reader (1 Point) All ledger accounts are closed to start the...
3.When closing entries are made:Immersive Reader (1 Point) All ledger accounts are closed to start the new accounting period. All real accounts are closed but not the nominal accounts. All balance sheet accounts are closed. All temporary accounts are closed but not the permanent accounts. All permanent accounts are closed but not the nominal accounts. 4.A wholesaler is an intermediary that buys products from manufacturers or other wholesalers and sells them to consumers.Immersive Reader (1 Point) True False 5.The Merchandise...
“Fana Lube” is a regional chain that provides a standard service for performing oil changes and...
“Fana Lube” is a regional chain that provides a standard service for performing oil changes and basic checkups on automobiles. The chain has a standard that says the average time per car for this service should be 15 minutes. There is considerable variability in times due to differences in layout of engines, degree of time pressure from other jobs, and many other sources. As a result, the management of the chain decided to study if the standard is being met...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT