Explanation Given information: The given function is f ( n 1 , n ) = n 2 − n 1 i f n 2 ≥ n 1 And f ( n 1 , n 2 ) = 0 i f n 2 < n 1 The given function is f ( n 1 , n ) = n 2 − n 1 i f n 2 ≥ n 1 And f ( n 1 , n 2 ) = 0 i f n 2 < n 1 And we have to construct a turning machine that computes the above function. For construction of machine we will follow below procedure: Firstly we represent f ( n 1 , n 2 ) on tapes as ( n 1 + 1 ) 1’s then a * and followed by ( n 2 + 1 ) 1’s Delete 1 from left of symbol * and for this deletion we also delete 1 from right of symbol * At any point of time if we have blank cell on left of symbol * then we have condition n 2 ≥ n 1 and we change this symbol * to 1 to get the final answer. At any point of time if we have blank cell on right of symbol * then we have condition n 2 < n 1 and we delete all cells to get the final answer 0. Based on above procedure we will now design the machine. Starting with below five Tuples: ( s 0 , 1 , s 1 , B , R ) , ( s 1 , 1 , s 1 , 1 , R ) , ( s 1 , * , s 2 , * , R ) , ( s 2 , B , s 7 , B , L ) , ( s 2 , 1 , s 3 , 1 , R ) , ( s 3 , 1 , s 3 , 1 , R ) , ( s 3 , B , s 4 , B , L ) , a n d ( s 4 , 1 , s 5 , B , L ) We begin at state s 0 , delete a 1 from left and go to right delete last 1 and go in state s 1 . After crossing symbol * we change state s 2 to check if next cell is blank. If it is blank then we go to state s 7 else we go to state s 3 and move to right side to delete 1. At state s 5 we move left to delete 1 and repeat same again with below Tuples: ( s 5 , 1 , s 5 , 1 , L ) , ( s 5 , * , s 6 , * , L ) , ( s 6 , B , s 8 , B , R ) , ( s 6 , 1 , s 9 , 1 , L ) , ( s 9 , 1 , s 9 , 1 , L ) , ( s 6 , B , s 0 , B , R ) Now we move to left in state s 5 and after crossing symbol * we change state to s 6 to check if the next cell is blank or not

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

8th Edition

ISBN: 9781259676512

Author: Kenneth H Rosen

Publisher: McGraw-Hill Education

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Chapter 13, Problem 30SE

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Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

Ch. 13.1 - Exercises 1-3 refer to the grammar with start...Ch. 13.1 - Exercises 1-3 refer to the grammar with start...Ch. 13.1 - Prob. 3E Ch. 13.1 - Let G=(V,T,S,P) be the phrase-structure grammar...Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Show that the grammar given in Example 5 generates...Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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To construct:

A turning machine that computes the given function using discrete mathematical methodologies.