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CS701 – Theory of Computation
Assignment No.1
Maximum marks: 50
Due Date: 9 November, 2017
Instructions
The purpose of this assignment is to give you hands on practice. It is expected that students will solve the assignment themselves. The Following rules will apply during the evaluation of assignment.
Cheating from any source will result in zero marks in the assignment.
Any student found cheating in any of the two assignments submitted will be awarded "F" grade in the course.
No assignment after due date will be accepted through email
Question No. 1 (Part1 = 5 + Part2 = 15+ snapshots=5) =25 marks)
Part 1.) Suppose we will take a following Diophantine equation as an input, show that given equation has solution in positive integers.
33x + 15y = 14.
Part 2.) Design a Turing machine in the following three ways of descriptions that decide the language L = {03n+1 : n ≥ 0}, the language consisting of all strings of 0s in given exponential function.
1. The Formal description of Turing machine
2. Implementation level descriptions of the Turing machine
3. High level description of the Turing machine
Note: Turing Machine must be creating in JFLAP software. The tutorial link of JFLAP has already been sent via course announcement. The snapshots of Turing machine diagram and testing accepting/rejecting strings must be pasted in assignment.
Virtual University of Pakistan MS (CS), Fall 2017
Question No. 2 (15+10=25 marks)
Read the research paper entitled “Comments on some theories of fuzzy computation”
and answer the following questions:
1) How can you differentiate and analysis between Turing Machine and Fuzzy
Turing Machine as discussed in the paper? Elaborate it critically in your own
words.
2) What functionalities have been expressed in extended Church thesis?
Elaborate it critically in your own words.
Please download above Research paper which has attached with zip file.
Note:
Plagiarism will be checked for each question. Please answer the questions in your own
words and marks will be awarded on the basis of your answer and plagiarism report.
For any query about the assignment, contact at CS701@vu.edu.pk
Tags:
Describe and Design a Turing machine in following three ways description that decide the following language
Solution
if we put n=0 then in put string will be
if we put n= 2 then the input string will be
2. 000000000
if we put n= 3 then the input string will be
3. 000000000000000000000000000
Formal Description of Turing Machine 0^3^n+1
A Turing machine M1 that decides the language given in question above is defined by the following 7-Tuple.
M = (Q, Σ, Γ, δ, q1, qaccept , qreject)
Q = (q1, q2, q3 … q7, qaccept , qreject)
q1 is start state, qaccept is the accept state and qreject is the reject state.
Σ = {0} // Input alphabet
Γ = {0, x, []} // tape or work alphabet where Σ⊆Γ and ∈ Γ.
δ : (Q × Γ) → (Q × Γ × {L, R}) // The transition function is described by the following state diagram.
Note: You may verify.. up to me its correct version
Question No 2
CS701 Assignment Qustion No 1 Solution – by- Ghulam Shabbir
Sol.
Ax+By=C
Coefficient ko comapre karain with given equation 33x+15y=14
A=33
B=15
C=14
The greatest common factor (GCR) of A and B must be divisible by C
GCF of A and B is 3
33/3=11
And
15/3=5
But this 3 is not not divisible by 14
As
14/3===not divisible
hence the given statement has no integer solution
Why you have put Q value till Q7 why not till Q5? Can you explain this point?
plz Q2 part one plzzzzzzzzzz
Question No 2
CS701 Assignment Qustion No 1 Solution
Sol.
Ax+By=C
Coefficient ko comapre karain with given equation 33x+15y=14
A=33
B=15
C=14
The greatest common factor (GCR) of A and B must be divisible by C
GCF of A and B is 3
33/3=11
And
15/3=5
But this 3 is not not divisible by 14
As
14/3===not divisible
hence the given statement has no integer solution
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