Please help me quickly ExerciseThe longest palindromic subsequence problem is a classic variation of the Longest CommonSubsequence (LCS) problem. The idea is to find LCS of the given string with its reverse, i.e., call LCS(X,reverse(X)) and the longest common subsequence will be the longest palindromic subsequence.1- We consider the sequence X = ABBDCACB. Apply the appropriate dynamic programmingalgorithm to compute the longest palindrome sequence and it is length. You must show all thecomputing steps.Exercise 2Find an optimal solution for the knapsack instance n (number of objects) -7 and W (total weight) -15, insuch a way that the total weight is less than or equal to a given limit and the total profit value is aslarge as possible. Profits and weights of each object are as follows(p1, p2p7)(10, 5, 15, 7, 6, 18, 3)(w1, w2.........w7) = (2,3,5,7,6,4,1)

Exercise:To solve the Longest Palindromic Subsequence (LPS) problem for the given sequence X =…

Answered: Exercise The longest palindromic…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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2) Is aa distinguishable from bb with respect to the set of strings over {a,b} that have an even number of a's? If so, prove it.
Let M be the language of all binary strings that contain the substring 11 and whose number of 0’s is even. (For example, 0101100 is in M.) (a) Give a largest possible set of strings that are pairwise distinguishable with respect to M. (b) Give a largest possible set of strings that are pairwise indistinguishable with respect to M.
4. Show that it is undecidable if every string in the langauge of a TM has even length.
A computer system considers a string of the digits 0, 1, 2, 3 a valid codeword if it has no two consecutive 1's. For example 01213 is a valid codeword of length 5 while 11320, 1022110, and 211133 are not valid. Let an be the number of valid codewords of length n. Find a recurrence relation for an and hence use it to find a4..
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.
Create an algorithm for parallel regularity testing.Input: a set S of permutation group G generators on;The output indicates whether G is regular or not.
IN SML USE PATTERN MATCHING Implement a function lessThan that compares two fractions x and y and returns true if x is less than y and returns false otherwise. For example,lessThan((2,3) (3,4)) returns true since 2/3 ≤3/4
(V, E) be a connected, undirected graph. Let A = V, B = V, and f(u) = neighbours of u. Select all that are true. Let G = a) f: AB is not a function Ob) f: A B is a function but we cannot always apply the Pigeonhole Principle with this A, B Odf: A B is a function but we cannot always apply the extended Pigeonhole Principle with this A, B d) none of the above
LetΣ={a,b}. Let L be the set of all strings over Σ that end in the substring bbbb. Give three strings in Σ∗ that are pairwise distinguishable with respect to L. Show that they are pairwise distinguishable by providing appro- priate distinguishing strings.
Minimize using K- map the logical funclion F(x,Y,z)= SoP C1,3,5,4) ?
A palindrome is a nonempty string over some alphabet that reads the same forward and backward. For instance, sequence ACGTGTCAAAATCG has palindromic subsequences, including ACGCA and CAAC, while ACG is not palindromic. Design an efficient algorithm that takes a sequence x[1 … n] and returns the longest palindromic subsequence. Give the Big-Oh characterization of your algorithm.
Let M be a FSM with n states. Let p and q be distinguishable states of M and let x be a shortest string distinguishing p and q. How long can the string x be as a function of n?

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