Exercise 21. Let M be the following Turing machine:1Input alphabet: E = {0,1}Tape alphabet: T= {0,1,U}Set of states:91,0, R | q1,0, R91,0, R | q1,0, R | q2, U, L42 41,0, R%3DQ = {qo, 91, 42, Ta, qr}la92, U, LFor each statement indicate whether it is true or false.1. M loops on all inputs.2. M loops on some inputs.3. The language accepted by M is not empty.

According to the given condition in question: 1. M loops on all inputs: False 2. M loops on some…

Answered: Exercise 2 1. Let M be the following…

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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1- Suppose a genetic algorithm uses chromosomes of the form X = abcdefgh with a fixed length of eight genes. Each gene can be any digit between 0 and 9. Let the fitness of individual X be calculated as: f(X) = (a + b)−(c+d) + (e+f) - (g+h) Let the initial population consist of 6 following chromosomes: X1 65413532 X2=87126601 X3 239 21285 X4=41852094 X5 83931775 X6=52769863 Evaluate the fitness of each individual (show all stages). Then select 4 of them for next generation and write chromosomes which are selected. (Consider maximization.) I. II. III. Perform the following crossover operation on the initial population: Do crossover on X2 and X6 (parents) and name offspring as X7 and X8. Consider one-point crossover and the crossover point between "c" and "d". Write chromosomes X7 and X8. Evaluate offspring generated by crossover operation above (Chromosomes X7 and X8). Do their fitness are better than their parents?
Exercise 2 Let M be the following Turing machine: 1 Input alphabet: E= {0, 1} Tape alphabet: T= {0,1,U} 9o | 91,0, R | qı,0, R q1,0, R| q1.0, R| Ф, Ц, L 91,0, R 91 Set of states: Q = {40, 91, 92, qa, Ir} 92 la L, L ,כ) For each statement indicate whether it is true or false. 1. M loops on all inputs. 2. M loops on some inputs. 3. The language accepted by M is not empty.
Suppose a genetic algorithm uses chromosomes of the form x = abcdefgh with a fixed length of eight genes. Each gene can be any digit between 0 and 9. Let the fitness of individual x be calculated as: f(x) = (a + b) – (c + d) + (e + f) – (g + h) and let the initial population consist of four individuals with the following chromosomes: x1 = 6 5 4 13 5 32 x2 = 87 126601 x3 = 2392 1 285 x4 = 4185 2094 1. Evaluate the fitness of each individual, showing all your workings, and arrange them in order with the fittest fiırst and the least fit last. 2. Perform the following crossover operations: One-point crossover, Two-point crossover, and uniform crossover.
1- Suppose a genetic algorithm uses chromosomes of the form X = abcdefgh with a fixed length of eight genes. Each gene can be any digit between 0 and 9. Let the fitness of individual X be calculated as: f(X) = (a + b)-(c+d) + (e+f) - (g+h) Let the initial population consist of 6 following chromosomes: I. II. III. X1 65413532 X2=87126601 X3=23921285 X4 418 52094 X5 83 931775 X6=52769863 Evaluate the fitness of each individual (show all stages). Then select 4 of them for next generation and write chromosomes which are selected. (Consider maximization.) Perform the following crossover operation on the initial population: Do crossover on X2 and X6 (parents) and name offspring as X7 and X8. Consider one-point crossover and the crossover point between "c" and "d". Write chromosomes X7 and X8. Evaluate offspring generated by crossover operation above (Chromosomes X7 and X8). Do their fitness are better than their parents?
Suppose a genetic algorithm uses chromosomes of the form x = abcdefah with a fixed length of eight genes. Each gene can be any digit between 0 and 9. Let the fitness of individual x be calculated as: f(x) = (a + b) - (c + d) + (e + f) - (g + h) and let the initial population consist of four individuals with the following chromosomes: x1 = 6 5 4 1 3 5 3 2 x2 = 8712660 1 x3 = 239 21285 x4 = 41852094 a) Evaluate the fitness of each individual and arrange them in order with the fittest First and the least at last. b) Perform the following crossover operations: Cross the Fittest two individuals using one-point crossover at the middle point. ii. i. Cross the second and third Fittest individuals using a two-point crossover (points b and f). Cross the First and third fittest individuals (ranked 1st and 3rd) using a ii. uniform crossover. [In the simplest case uniform crossover means just a random exchange of genes between two parents. For example, we may swap genes at positions a, d and f of…
Suppose a Genetic Algorithm uses chromosomes of the form x=abcdef with a fixed length of six genes.Each gene can be any digit between 0 and 9 . Let the fitness of individual x be calculated as : f(x) =(a+b)-(c+d)-(e+f) And let the initial population consist of four individuals x1, ... ,x4 with the following chromosomes : x1 = 3 5 3 2 6 5, x2 = 9 8 0 1 2 2, x3 = 1 2 2 1 2 3, x4 = 7 9 2 3 1 1 1. 1.Evaluate the fitness of each individual, showing all your workings, and arrange them in order with the fittest first and the least fit last. 2. calculate the average fitness. 3. Perform the following crossover operations:a- Cross the fittest two individuals using one point crossover at the middle point.b- Cross the second and third fittest individuals using a two point crossover (points b and e). Suppose the new population consists of the four offspring individuals received by the crossover operations in the above question. Evaluate the fitness of the new population, showing all your…
Suppose you have a Turing machine M with E = {D,U,}, Q = {qo, 91}, and S is given by the table: q og o direction 90/ q1u R Describing instructions What is the sentence describing the second instruction 8(90, u) = (9o, U,M) of M? Use A(x,y) to abbreviate the formula A(x, y). ВР8.2 8(q0, u) = (q0,u, N) Submit O 6(q0, L) = (q0, u, N)
Q1. Design a Turing machine to count number of l's in the tape and write the output at beginning of the tape. (Consider that tape has binary numbers only). Q2. Consider the TM defined by M = (Q. E,r, 8, q0, B, F) 8 ( qo, a ) = (q1, a , R) 8 ( qo , b ) = ( q1 , b, R) 8( qo, B) = (q1,B , R) 8(q1, a) = ( qo, a, L) 8(q1, b )= ( qo, b , L) 8 ( qı, B ) = ( qo, B, L) What is the state of TM on input 'ab'?
Computer Science provide a three-tape turing machine for L = a^n where n => 0 is perfect square. λ should be accepted. tape 1: string to be processed n^2 a's tape 2: strings of length n^2. These sequences will be made up of symbol Y tape 3: strings of length n. These sequences should be made up of symbol Y. Tape 2 and 3 recursively generated from string 1, only last string retained on tape.
Turing Machines 1. Let Turing machine, where Q = {q, 9, h}, E, = {a, b, o, 0}, and the transition function & is given by the following table: q o d(q, a) 9,a (q, b) q,b (q, a) 4,0 (h, D) 4.0 (q, -) 9,a (q, -) 9,b (q,-) 9,0 (9,-) 9,0 (9 -) (a) Trace the computation of M starting from the configuration (qo, aabbba). (b) Describe what M does when started in q, on any length of a tape.
Consider the following Turing machine M1: Y/Y R 96 B/BL B/B L qo B/B R Y/Y L a/a L 95 Y/Y R 91 94 Select one: O A. {q2mbn I m, n ≥ 1} O B. {a2nbIn >0} O C. {a²mbn|m, n ≥ 0} O D. {a²nbInz 0} a/X R X/X R b/Y L What is the language for Machine MI? 92 a/X R 93 a/a R Y/Y R
For example, in the following simple Turing Machine, the operation may never halt (infinite loop): Turing Machine M = (S, E, 8, s, {h}) where S = {q, h} E = {a, u, } 8 is given by the following transition functions: 1. ((q, a) , (q, +)) 2. ((q, u) , (h, u)) 3. (q, >), (q, →)) Note: u represents the blank symbol.

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