Prove the the regular languages are closed under complement The complement of a language is all strings not in that language More formally, the complement of a language L , which can be written as L is defined as follows L Sigma L w w L ( Hint This proof can be relatively short Start from the fact that if a language is regular, then there exists a DFA that recognizes that language Then show how to construct a machine that recognizes the complement of that language )

The Answer is in the image, click to view ...

Question: Prove the the regular languages are closed under complement. The complement of a language is all strings not in that language. More formally, the complement

Prove the the regular languages are closed under complement. The complement of a language is all strings not in that language. More formally, the complement of a language L

,

which can be written as L is defined as follows: L

= \

Sigma

= {

} . (

Hint: This proof can be relatively short. Start from the fact that if a language is regular, then there exists a DFA that recognizes that language. Then show how to construct a machine that recognizes the complement of that language.

)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

true or false 21 Uncountable infinity (for example, the cardinality of the real numbers). No Countable infinity (for example, the cardinality of the integers) E' All strings over the alphabet ?. ??...

Problem 1 In class, we showed that if M is a DFA that recognizes language A, swapping the accepting and nonaccepting states yields a new DFA recognizing the complement of A. We then concluded that...

3. [10pt] Show that the class of regular languages is closed under complement. Hint: Prove that given a DFA M that accepts a language L(M) CE", swapping the accept and nonaccepting states in M yields...

Problem 3: Complement and Intersection (a) Use the results of homework 2 problem 5(a) to prove that Regular Languages are closed under complement. (b) Note that for any sets S, and S2, the...

Text Exercise 1 . 9 . Prove that every NFA can be converted to an equivalent one that has a single accept state. Text Exercise 1 . 1 0 . a . Show that if M is a DFA that recognizes language B ,...

Note: L c denotes the complement of L. 1. Find regular expressions for the following languages: a) L = {a n b m : n 3, m is odd} b) L = {a n b m : n + m is odd} c) L = {w {a, b}* : |w| mod 3 0} 2....

1. Recall that a left-linear grammar is a grammar in which all non-terminals (i.e. variables) are on the left end of the right side of production rules, while a right-linear grammar is a grammar in...

Nondeterminism 5. Give an NFA with the specified number of states for recognizing each language below. In each case, I = {0, 1} (a) [7 pts) L1 = {w W contains an even number of Os or contains exactly...

If L 1 and L 2 are languages, the s ymmetric difference of L 1 and L 2 is the set L 1 L 2 = { x ( x L 1 (the complement of L 2) ) ( x (the complement of L 1) L 2)}. a. Prove, without constructing the...

If M is a DFA that recognizes language B , you can manipulate that accept and non - accept states of M to yield a new DFA, M ' , that recognizes the complement of B . A . ( 1 0 ) Determine the...

Eglon Mills has a new Year 2020 project with an initial equipment cost of $368,000 and a project life of 10 years. The firm generally uses straight line depreciation to a zero book value over the...

Discuss the meaning of R square in regression analysis. What does an R square of 1.00 mean?

What is fair value accounting, and how does it differ from historical cost accounting? Discuss the advantages of fair value measurement in providing current and relevant information to financial...

Scenario: A Multi-national Corporation called The Globe has created a subsidiary called Thirst in an under-developed country called non-potable waters. This hosting country suffers from a severe...

Is there a clear hierarchy of points in my outline?

B If you were on a jury in a criminal trial, what would your expectations for evidence be? Would you be willing to convict someone based on a fiber sample, even if the expert witness described it as...

2 Weve spent much of this chapter talking about the importance of outlining and of communicating your final outline clearly to your audience. How is that different from presenting your outline in...