Given two regular expressions r1 and r2, construct a decision procedure to determine whether the language of r1 is contained in the language r2; that is, the language of r1 is a subset of the language of r2.
Answer:
Test if L(M1-2) is empty.
Construct FA M2-1 from M1 and M2 which recognizes the language L(>M2) - L(>M1).
COMMENT: note we use the algorithm that is instrumental in proving that regular languages are closed with respect to the set difference operator.
Test if L(M2-1) is empty.
Answer yes if and only if both answers were yes.
Explanation:
An algorithm must be guaranteed to halt after a finite number of steps.
Each step of the algorithm must be well specified (deterministic rather than non-deterministic).
Three basic problems:
Given an FA M and an input x, does M accept x?
Is x in L(M)
Given an FA M, is there a string that it accepts?
Is L(M) the empty set?
Given an FA M, is L(M) finite?
Algorithm for determining if M accepts x.
Simply execute M on x.
Output yes if we end up at an accepting state.
This algorithm clearly halts after a finite number of steps, and it is well specified.
This algorithm is also clearly correct.
Testing if L(M) is empty.
Incorrect "Algorithm"
Simulate M on all strings x.
Output yes if and only if all strings are rejected.
The "algorithm" is well specified, and it is also clearly correct.
However, this is not an algorithm because there are an infinite number of strings to simulate M on, and thus it is not guaranteed to halt in a finite amount of time.
COMMENT: Note we use the algorithm for the first problem as a subroutine; you must think in this fashion to solve the problems we will ask.
Correct Algorithm
Simulate M on all strings of length between 0 and n-1 where M has n states.
Output no if and only if all strings are rejected.
Otherwise output yes.
This algorithm clearly halts after a finite number of steps, and it is well specified.
The correctness of the algorithm follows from the fact that if M accepts any strings, it must accept one of length at most n-1.
Suppose this is not true; that is, L(M) is not empty but the shortest string accepted by M has a length of at least n.
Let x be the shortest string accepted by M where |x| > n-1.
Using the Pumping Lemma, we know that there must be a "loop" in x which can be pumped 0 times to create a shorter string in L.
This is a contradiction and the result follows.
COMMENT: There are more efficient algorithms, but we won't get into that.
Testing if L(M) is finite
Incorrect "Algorithm"
Simulate M on all strings x.
Output yes if and only if there are a finite number of yes answers.
This "algorithm" is well specified and correct.
However, this is not an algorithm because there are an infinite number of strings to simulate M on, and thus it is not guaranteed to halt in a finite amount of time.
COMMENT: Note we again use the algorithm for the first problem as a subroutine.
Correct Algorithm
Simulate M on all strings of length between n and 2n-1 where M has n states.
Output yes if and only if no string is accepted.
Otherwise output no.
This algorithm clearly halts after a finite number of steps, and it is well specified.
The correctness of the algorithm follows from the fact that if M accepts an infinite number of strings, it must accept one of length between n and 2n-1.
This builds on the idea that if M accepts an infinite number of strings, there must be a "loop" that can be pumped.
This loop must have length at most n.
When we pump it 0 times, we have a string of length less than n.
When we pump it once, we increase the length of the string by at most n so we cannot exceed 2n-1. The problem is we might not exceed n-1 yet.
The key is we can keep pumping it and at some point, its length must exceed n-1, and in the step it does, it cannot jump past 2n-1 since the size of the loop is at most n.
This proof is not totally correct, but it captures the key idea.
COMMENT: There again are more efficient algorithms, but we won't get into that.
Other problems we can solve using these basic algorithms (and other algorithms we've seen earlier this chapter) as subroutines.
COMMENT: many of these algorithms depend on your understanding of basic set operations such as set complement, set difference, set union, etc.
Given a regular expression r, is Lr finite?
Convert r to an equivalent FA M.
COMMENT: note we use the two algorithms for converting a regular expression to an NFA and then an NFA to an FA.
Test if L(M) is finite.
Output the answer to the above test.
Given two FAs M1 and M2, is L(M1) = L(M2)?
Construct FA M1-2 from M1 and M2 which recognizes the language L(>M1) - L(>M2).
COMMENT: note we use the algorithm that is instrumental in proving that regular languages are closed with respect to the set difference operator.
Test if L(M1-2) is empty.
Construct FA M2-1 from M1 and M2 which recognizes the language L(>M2) - L(>M1).
COMMENT: note we use the algorithm that is instrumental in proving that regular languages are closed with respect to the set difference operator.
Test if L(M2-1) is empty.
Answer yes if and only if both answers were yes.
How are dates and times stored by Excel?
Answer:
Regardless of how you have formatted a cell to display a date or time, Excel always internally stores dates And times the same way. Excel stores dates and times as a number representing the number of days since 1900-Jan-0, plus a fractional portion of a 24 hour day: ddddd. tttttt
Explanation:
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The _________ attack exploits the common use of a modular exponentiation algorithm in RSA encryption and decryption, but can be adapted to work with any implementation that does not run in fixed time.
A. mathematical.
B. timing.
C. chosen ciphertext.
D. brute-force.
Answer:
chosen ciphertext
Explanation:
Chosen ciphertext attack is a scenario in which the attacker has the ability to choose ciphertexts C i and to view their corresponding decryptions – plaintexts P i . It is essentially the same scenario as a chosen plaintext attack but applied to a decryption function, instead of the encryption function.
Cyber attack usually associated with obtaining decryption keys that do not run in fixed time is called the chosen ciphertext attack.
Theae kind of attack is usually performed through gathering of decryption codes or key which are associated to certain cipher texts The attacker would then use the gathered patterns and information to obtain the decryption key to the selected or chosen ciphertext.Hence, chosen ciphertext attempts the use of modular exponentiation.
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computer is an ............. machine because once a task is intitated computer proceeds on its own t ill its completion.
Answer:
I think digital,versatile
computer is an electronic digital versatile machine because once a task is initiated computer proceeds on its own till its completation.
Heinrich Koch is a second-year college student. Last semester his best friend had his laptop stolen. The laptop was an old computer that he planned to replace soon, but the greatest loss was his data: he had not performed a backup and all his data was lost. Heinrich himself does not perform data backups but knows that he needs to do that on a regular basis. He has decided to use an online backup service that will automatically back up his data whenever it changes. Evaluate and compare reviews of online backup services. Consider iDrive, Carbonite, Acronis True Image, BackBlaze, and others you might find in your research. Recommend a service that you consider the best solution for Heinrich. Discuss your reviews and mention speed, security, and features in your recommendation.
Answer:
Acronis True Image is the one I would recommend out of these mentioned online backup services.
Explanation:
The evaluations and reviews of each of the online backup services are as follows:
a. iDrive
For this, we have:
Speed = 60% - fair
Security = 100% - excellent
Privacy = 88% - very good
Features = 95% - excellent
Pricing = 85% - Very good
Because of its various features, pricing, and usability, IDrive reviews suggest that it is a very efficient online backup solution. However, there have been complaints concerning its speed and the fact that there are no monthly plans available.
b. Carbonite
For this, we have:
Speed = 60% - fair
Security = 100% - excellent
Privacy = 87% - very good
Pricing = 85% - very good
File backup and restoration = 75% - good
Carbonite reviews reveal that it is simple to use and provides limitless backup for one device. The main drawback is that it has extremely poor backup speeds.
c. Acronis True Image
This is fast, simple and intuitive
It has complete control over the backup updates, including how and when they occur.
It is not expensive.
Acrnonis True image is a powerful backup storage service. It enables data and file backup and restoration from USB drives.
Many reviewers of Acrnonis True image have stated that they have had no issues with its service, that it is worth purchasing, and that there are no concerns.
d. Backblaze
For this, we have:
Speed = 75% - good
Security = 75% - good
Privacy = 70% - decent
Pricing = 100% - excellent
Support = 95% - excellent
Features = 65% - decent
File back-up and restoration = 70% - decent
Backblaze is one of the most popular internet backup services. This storage service, however, does not allow for ustomization.
Recommendation
Acronis True Image is the one I would recommend out of these mentioned online backup services. This is due to the fact that it delivers a large amount of accurate and high-quality data storage. It is quick, simple and intuitive, which is what most people care about. Furthermore, reviewers have stated that this service is quite effective and that there have been very few issues with it. The other services demonstrate that their services have flaws, such as lack of customization and slowness.
