Solutions: Tutorial 2
August 11, 2015
1. Let X = cfw_< M, w >  M is a single tape Turing Machine that never
modies the portion of the tape containing the input w. Is X decidable?
Prove your answer.
Answer : We will prove by contradiction that X is undeci
Discrete Mathematical
Structures
Sixth Edition
.
Bernard Kolman
Drexel University
.
RobertC. Busby
Drexel University
.
Sharon Cutler Ross
Georgia Perimeter College
Upper Saddle River, NJ 07458
11.3
11.3
PublicKeyCryptology
449
Public KeY1Cryptoiogy
In 197
Artificial Intelligence (CS60045)
Assignment 2 (Theory)

Name:
Roll Number:
Answer the following questions and submit it as a pdf file in moodle.
This assignment should be submitted by 11th August, 2016.
Q1:
Describe in brief a Robot soccer player as an
Artificial Intelligence (CS60045)
Assignment 1
Name: Kumar Ayush
Roll Number: 13CS10058
Name of the AI System : Collaborative TV Viewing Assistant
Sensors: Voice Recorder(Speech to Text)
Input: Voice of viewers (one viewer at a time) speech is converted t
Artificial Intelligence (CS60045)
Assignment 2 (Programming assignment)

Name:
Roll Number:
Read the following problem and implement it using any language of
your choice (C, C+ , Java or Python). Submit a Report on this
problem along with your codes. Als
Solutions: Tutorial 6
September 8, 2015
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Independent Set:
Independent Set NP Assume the verier is presented with a subset
S of vertices in G. Our verier will check that S indeed contains at least
k vertices
Solutions: Tutorial 4
1. Give the model of the sentence.
eq = x[R1 (x, x)]
x, y[R1 (x, y) R1 (y, x)]
x, y, z[(R1 (x, y) R1 (y, z) = R1 (x, z)]
Answer : The statement eq gives the three conditions of an equivalence relation. A model
(A, R1 ), where A is
Solutions: Tutorial 4
August 25, 2015
1. Let Lf in = cfw_< M > L(M ) is nite. Prove using Recursion theorem
that Lf in is undecidable.
Answer : Let Lf in be decidable and be decided by the TM D. Let us
dene two new machines N1 and N2 as follows.
N1 : on
Solutions : Tutorial 3
August 12, 2015
1. In the silly Post Correspondence Problem, SPCP, in each pair the top
string has the same length as the bottom string. Show that the SPCP is
decidable.
i
Answer: Let cfw_ ui be an instance of SPCP. We claim that :
THEORY OF COMPUTATION CS41001
Tutorial 5 Homework Problem Solutions
September 1, 2015
1. Let us consider the w given as = [x p(x, x) x, y, z (p(x, y) p(y, z) =
p(x, z) x, y (p(x, y) p(y, x)] = yx p(y, x). Prove that for any model
M = (D,p), if D is nite,
THEORY OF COMPUTATION CS41001
Tutorial 5 Classroom Problem Solutions
September 1, 2015
1. Let DOUBLE SAT = cfw_  such that has at least two satisfying assignments.
Show that DOU BLE SAT is NPcomplete.
Soln: DOU BLE SAT N P the certicate is a pair of ass
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Solutions : Tutorial 3
August 19, 2015
1. Let L = cfw_< M > L(M ) = . Prove that L is not Turingrecognizable.
Answer: Let L be Turingrecognizable by the TM R. We will construct
a decider D for HT M (halting problem) using R.
D : on input < M, w >
(a)
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