o Construct a Standard Turing Machine to compute the function f(x) = [1. the ceiling of ▪ Assume is a positive integer represented in unary notation on the Turing machine's tape. • f(x) will also be a positive integer represented in unary notation on the Turing machine's tape. o Save your Standard Turing Machine as a JFLAP jff file, and submit that .jff file to Canvas as your solution to this exercise. zamples... o Example 1 • If x = 5, then f(x) = f(5) = [1 = [2.51 = 3 Turing machine input would be a string of five ones, which is the string 11111 Turing machine output should be a string of three ones, which is the string 111 o Example 2 If z = 8, then f(x) = f(8) = [1 = [4.01 = 4 Turing machine input would be a string of eight ones, which is the string 111111 Turing machine output should be a string of four ones, which is the string 1111 o Example 3 • If x= 15, then f(x) = f(15) = []=[7.51 = 8 ▪ Turing machine input would be a string of fifteen ones, which is the string 111111111111111 • Turing machine output should be a string of eight ones, which is the string 11111111 Example 4 If x = 6, then f(x) = f(6) = [1 = [3.0] =3 • Turing machine input would be a string of six ones, which is the string 111111 ▪ Turing machine output should be a string of three ones, which is the string 111

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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IS CACILIS...
o Construct a Standard Turing Machine to compute the function f(x) = [1,
the ceiling of
▪ Assume x is a positive integer represented in unary notation on the Turing machine's
tape.
▪ f(x) will also be a positive integer represented in unary notation on the Turing
machine's tape.
o Save your Standard Turing Machine as a JFLAP.jff file, and submit that .jff file to
Canvas as your solution to this exercise.
Examples...
Example 1
▪ If x = 5, then f(x) = f(5) = [1 = [2.5] =3
Turing machine input would be a string of five ones, which is the string 11111
Turing machine output should be a string of three ones, which is the string 111
• Example 2
If x = 8, then f(x) = f(8) = [1 = [4.0] =4
▪ Turing machine input would be a string of eight ones, which is the string 11111111
Turing machine output should be a string of four ones, which is the string 1111
o Example 3
• If x = 15, then f(x) = f(15) = [] = [ 7.5] = 8
▪ Turing machine input would be a string of fifteen ones, which is the string
111111111111111
Turing machine output should be a string of eight ones, which is the string
11111111
o Example 4
If x = 6, then f(x) = f(6) = [1 = [ 3.0] =3
■ Turing machine input would be a string of six ones, which is the string 111111
Turing machine output should be a string of three ones, which is the string 111
Transcribed Image Text:IS CACILIS... o Construct a Standard Turing Machine to compute the function f(x) = [1, the ceiling of ▪ Assume x is a positive integer represented in unary notation on the Turing machine's tape. ▪ f(x) will also be a positive integer represented in unary notation on the Turing machine's tape. o Save your Standard Turing Machine as a JFLAP.jff file, and submit that .jff file to Canvas as your solution to this exercise. Examples... Example 1 ▪ If x = 5, then f(x) = f(5) = [1 = [2.5] =3 Turing machine input would be a string of five ones, which is the string 11111 Turing machine output should be a string of three ones, which is the string 111 • Example 2 If x = 8, then f(x) = f(8) = [1 = [4.0] =4 ▪ Turing machine input would be a string of eight ones, which is the string 11111111 Turing machine output should be a string of four ones, which is the string 1111 o Example 3 • If x = 15, then f(x) = f(15) = [] = [ 7.5] = 8 ▪ Turing machine input would be a string of fifteen ones, which is the string 111111111111111 Turing machine output should be a string of eight ones, which is the string 11111111 o Example 4 If x = 6, then f(x) = f(6) = [1 = [ 3.0] =3 ■ Turing machine input would be a string of six ones, which is the string 111111 Turing machine output should be a string of three ones, which is the string 111
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