Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 32.1, Problem 2E
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Is aa distinguishable from the string a with respect to the set of strings over {a,b} that end with aaa? If so, prove it. *
What implication does the above result have on the design of an FSA M such that L(M) is the set of strings over {a,b} that end with aaa?
We consider certain strings of length 6 over the alphabet S = {A,B,C}.
We require that the string contains exactly two As, and exactly two B's, and exactly two C's.
How many such strings are there? That is, how many strings of length 6 over the alphabet {A,B,C} contains exactly two A's, two B's and two C's?
If a is a symbol and n > 0, then an denotes a···a, or in words, the string of length n consisting of only a’s. Now consider the coding with two code words 0n and 1n, for some natural number n > 0. Show that this coding is perfect if and only if n is odd.
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- Prove that EQDFA is decidable by testing the two DFAs on all strings up to a certain size. Calculate a size that works.arrow_forwardA Boolean function simplified by using k-map has in general more terms than the product of maxterms standard form ? True Falsearrow_forwardRegular Expression for the set of all even length strings with at most two 0’s? Show me step-by-step solution.arrow_forward
- Write an algorithm for addressing the subset-superset problem in string matching. That is, search a text with several strings, some of which are factors of others. do not return any strings that are factors of other test strings found in text (b) Repeat with text consisting of 100 appended copies of and the test itemsarrow_forwardIf the sequence number space is k bits large, you should seriously consider using both the selective-repeat technique and the Go-Back-N strategy in your search for a solution. What is the maximum allowable size for the sender window that we are allowed to make use of?arrow_forwardA problem on Theory of Computation. Draw an NFA over the alphabet (0,1) that accepts strings having a '0' at every even position.arrow_forward
- Show that the language of strings over {1} of the form 1^n where n is a Fibonacci number is not regular.arrow_forwardprove the assertion. In the worst scenario, it takes time proportional to NM to determine if an N-character text string recognised by the NFA corresponds to an M-character RE.arrow_forwardIf the sequence number space is large enough to include k bits of information, you should carefully consider employing both the selective-repeat technique and the Go-Back-N strategy while searching for a solution. What is the biggest size that the sender window that we are allowed to use may be in total?arrow_forward
- Let E={〈M〉| M is a TM and every string in L(M) has even length}. Argue that the property described in E is not trivial – i.e., that Rice’s theorem applies to E.arrow_forwardWhen trying to find a solution, you should give serious attention to employing both the selective-repeat technique and the Go-Back-N strategy if the sequence number space is wide enough to incorporate k bits of information. If the sequence number space is not big enough, you should not even bother trying to find a solution. In its whole, what is the maximum size that the sender window that we are allowed to use is authorised to be allowed to be?arrow_forwardShow how the Boyer-Moore string matching algorithm works for the following input.How many comparisons of characters are done in each case?(a) T = AAAAAAAAAA, P = AAAB(b) T = ratsbatsandcats, P =cathatarrow_forward
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