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 32.3, Problem 1E
Program Plan Intro
To construct string matching automation for pattern
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Find the prefix function of KMP string matching algorithm for the following pattern "lalalaland"
Construct a finite-automaton using the alphabet {a,b} for the pattern abbaba to be used in string matching. Show the exact sequence of steps when using the finite-automaton to find all occurrences of the pattern in the text babbababbaba.
Draw the binary expression trees for the following:a) 4 * (5 – 9) + 9 * 8 -1 * (3 + 5 -2)
b) x * (a / b * c – g * s / u)
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- Implement a lexicographically smallest topological ordering in the C languagearrow_forwardRegular grammar, S ⟶⟶ aS | bS |a | bb, will generate the following language L: Group of answer choices: A)L = L ((a +b)* (a + bbb)) b)L = L ( a(a + b)*bb) c)L = L ( (bb + a) (a + b)*) D)L = L ((a + b)* (a + bb))arrow_forwardFor each of the following patterns (for string matching), give the Knuth-Morris-Pratt lpstable that would be created by pre-processing the pattern under each respective algorithm.(a) AABABBA(b) DRABDRAD(c) CRONOCROarrow_forward
- Can you describe an algorithm that given two context-free grammars G1 and G2 outputs YES if andonly if every string generated by G1 is also generated by G2. (I.e., output YES exactlywhen the set of strings generated by G1 is a subset of the set of strings generated by G2.)arrow_forwardConsider the Grammarbexpr ( bexpr or bterm | btermbterm ( bterm and bfactor | bfactorbfactor ( not bfactor | (bexpr) | true | falseConstruct a parse tree for the sentence not(true or false)arrow_forwardDraw an equivalent DFA for the language “All possible strings that has two or three 1’s over ∑ = {0 , 1}” and also write down an equivalent regular expression for the language "All possible strings whose each a is followed by double b’s over ∑ = {a , b}.arrow_forward
- Describe an algorithm that given two context-free grammars G1 and G2 outputs YES if and only if every string generated by G1 is also generated by G2. (I.e., output YES exactly when the set of strings generated by G1 is a subset of the set of strings generated by G2.) Would such an algorithm be possible? why or why notarrow_forwardImplement a more extensive finite-state grammar for noun groups by using the examples given in Section 13.5 and test it on some NPs. Use an on-line dictionary with parts-of-speech if available; if not, build a more restricted system by hand.arrow_forwardWrite a deterministic automaton to recognize the language over {a, b, c}* such that every string of a’s must be followed by at least two c’s and every string of c’s must be followed by at least three b’s. {accepted strings: accbbb , aaacccbbbcbbb }arrow_forward
- Can you think of a good example of a Boyer-Moore string search algorithm implementation in the literature? Explain how to put the plan into action.arrow_forwardComputer Science Consider the following two grammars with alphabet a and b i. (b*ab*a)*b* ii. (b*ab*a)*b*(b*ab*a)*b* Are there any strings are generated by one of the grammars and cannot be generated by the other? If there are more than one such string, how do you describe them.arrow_forwardWrite down an equivalent regular expression for the language "All possible strings whose each a is followed by double b’s over ∑ = {a , b}.Draw an equivalent DFA for the language “All possible strings that has two or three 1’s over ∑ = {0 , 1}”.arrow_forward
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