Cs6503 theory of computation may june 2016 be cse anna university question paper

Jun 27, 201612 likes6,554 views

This document contains questions from a Computer Science and Engineering exam on the theory of computation. It covers topics like finite automata, context-free grammars, pushdown automata, Turing machines, and more. Students are asked to construct various computational models, prove properties like pumping lemmas, minimize deterministic finite automata, derive strings, and determine whether problems are tractable or intractable. The exam tests understanding of fundamental concepts in formal languages and automata theory.

Reg. No. :
B.E. / B.Tech. DEGREE EXAMINATION, MAY / JUNE 2016
Fifth Semester
Computer Science and Engineering
CS6503 THEORY OF COMPUTATION
(Regulation 2013)
Time : Three hours Maximum : 100 marks
Answer ALL Questions
Part A – (𝟏𝟎 × 𝟐 = 𝟐𝟎 marks)
1. Draw a non-deterministic finite automata to accept strings containing the substring 0101.
2. State the pumping lemma for regular languages.
3. What do you mean by null production and unit production? Give an example..
4. Construct a CFG fro set of strings that contain equal number of a‟s and b‟s over Σ={a, b}.
5. Does a Push down Automata have memory? Justify.
6. Define Push down Automata.
7. What are the differences between a Finite automata and a Turing machine?
8. What is Turing machine?
9. When is a Recursively Enumerable language said to be Recursive?
10. Identify whether „Tower of Hanoi‟ problem is tractable or intractable. Justify your answer.
Part B – (5 × 𝟏𝟔 = 𝟖𝟎 marks)
11 (a) (i) Construct a NFA that accepts all strings hat end in 01. Give its transition table and
extend transition function for the input string 00101. Also construct a DFA for the
above NFA using subset construction method. (10)
(ii) Prove the following by principle of induction. 𝑥2𝑛
𝑥=1 =
𝑛 𝑛+1 (2𝑛+1)
6
. (6)
Or
(b) (i) What is Regular Expression? Write a regular expression for set of strings that
consists of alternating 0‟s and 1‟s. (8)
(ii) Write and explain the algorithm for minimization of a DFA. Using the above
algorithm minimize the following DFA. (8)
A
0 1start
B C D
0
1
0
E
1 1
F G D
0
0
01
1
1
1 0
0
Question Paper Code : 57255

12 (a) (i) Construct a reduced grammar equivalent to the grammar G = (N, T, P, S) where,
N = {S, A, C, D, E} (6)
T = {a, b}
P = { S → aAa, A → Sb, A → bCC, A → DaA, C → abb, C → DD, E → aC,
D → aDA}.
(ii) When is a grammar said to be ambiguous? Explain with the help of example. (5)
(iii) Show the derivation steps and construct derivation tree for the string „ababbb‟. (5)
by using left most derivation with the grammar.
S → AB | ε
A→ aB
B→ Sb
Or
(b) (i) What is the purpose of normalization? Construct the CNF and GNF for the
following grammar and explain the steps. (10)
S → aAa | bBb | ε
A→ C | a
B→ C | b
C→ CDE | ε
D→ A | B | ab
(ii) Construct a CFG for the regular expression (011+1) (01). (6)
13 (a) (i) Construct a Push down Automata to accept the following language L on Σ={a, b}
by empty stack. 𝐿 = {𝑤𝑤R
| 𝑤 ∈ 𝛴+
}. (10)
(ii) What is an instantaneous description that the PDA? How will you represent it?
Also give three important principles of ID and their transactions. (6)
Or
(b) (i) Explain acceptance by final state and acceptance by empty stack of a Push down
Automata. (8)
(ii) State the pumping lemma for CFL. Use pumping lemma to show that the
language 𝐿 = {𝑎i
𝑏j
𝑐k
| 𝑖 < 𝑗 < 𝑘} is not a CFL. (8)
14 (a) (i) Construct a Turing Machine to accept palindromes in an alphabet set Σ={a, b}.
Trace the string “abab” and “baab”. (8)
(ii) Explain the variations of Turing Machine. (8)
Or
(b) (i) Explain Halting problem. Is it solvable or unsolvable problem? Discuss. (8)
(ii) Describe the Chomsky hierarchy of languages with example. What are the
devices that accept these languages? (8)
15 (a) What is Universal Turing Machine? Bring out its significance. Also construct a
Turing Machine to add two numbers and encode it. (16)
Or
(b) What is post correspondence problem (PCP)? Explain with the help of an
example. (16)
All the Best – No substitute for hard work.
Mr. G. Appasami SET, NET, GATE, M.Sc., M.C.A., M.Phil., M.Tech., (P.hd.), MISTE, MIETE, AMIE, MCSI, MIAE, MIACSIT,
MASCAP, MIARCS, MISIAM, MISCE, MIMS, MISCA, MISAET, PGDTS, PGDBA, PGDHN, PGDST, (AP / CSE / DRPEC).

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This document outlines important questions from 5 units that could appear on the CS64O2 DESIGN AND ANALYSIS OF ALGORITHMS exam. Unit I covers algorithm problem types, problem solving fundamentals, asymptotic notations, and analyzing recursive/non-recursive algorithms. Unit II discusses closest pair, convex hull, TSP, KP, sorting algorithms, and binary search. Unit III is about dynamic programming, graph algorithms, OBST, and HMT. Unit IV is linear programming problems. Unit V covers complexity classes, backtracking, branch and bound, and approximation algorithms for NP-hard problems like TSP and KP. The document provides guidance on questions to study for the exam.

Cs6702 graph theory and applications question bankappasami

This document contains questions and answers related to the course CS6702 Graph Theory and Applications. It is divided into 6 units which cover topics like introduction to graphs, trees, connectivity, planarity, graph colorings, directed graphs, permutations and combinations, and generating functions. For each unit, it lists short answer questions in Part A and longer proof or explanation questions in Part B. The questions test concepts fundamental to graph theory such as definitions of graphs, trees, connectivity, colorings, isomorphism, and counting methods applied to graph theory.

Cs6702 graph theory and applications Anna University question paper apr may 2...appasami

This document contains a past exam paper for the subject "Graph Theory and Applications". It includes 15 multiple choice and long answer questions covering topics such as Euler graphs, planar graphs, spanning trees, matchings, counting principles, and graph algorithms. The key provided contains concise definitions and explanations for the concepts and steps to solve problems in 3 sentences or less.

Cs6503 theory of computation lesson planappasami

This document contains a lesson plan for the subject "Theory of Computation" taught to 5th semester Computer Science students. The lesson plan spans 9 weeks and covers 5 units - Finite Automata, Grammars, Pushdown Automata, Turing Machines, and Unsolvable Problems. It lists the topics to be covered in each class, the relevant textbook chapters and pages, and the faculty member responsible for teaching the subject. The lesson plan provides a comprehensive overview of the topics, readings, and schedule for the Theory of Computation course.

Cs6503 theory of computation syllabusappasami

This document outlines the course objectives and units for a Theory of Computation course. The course covers various computing models like finite state machines, pushdown automata, and Turing machines. It examines decidability and undecidability of problems. Key topics include regular languages and expressions, context-free grammars, pumping lemmas, Turing machines, and analyzing complexity classes like P and NP-complete problems. The course aims to help students understand these foundational models of computation and analyze problem solvability.

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Cs6402 design and analysis of algorithms may june 2016 answer keyappasami

The document discusses algorithms and complexity analysis. It provides Euclid's algorithm for computing greatest common divisor, compares the orders of growth of n(n-1)/2 and n^2, and describes the general strategy of divide and conquer methods. It also defines problems like the closest pair problem, single source shortest path problem, and assignment problem. Finally, it discusses topics like state space trees, the extreme point theorem, and lower bounds.

Cs6702 graph theory and applications syllabusappasami

The document outlines the objectives and units of a course on Graph Theory and Applications. The 5 units cover topics such as graphs, trees, connectivity, planarity, matrices, coloring, permutations, combinations, and generating functions. Students will learn fundamental graph theory topics and results, techniques of proofs and analysis, and be able to write precise definitions, construct examples, and prove mathematical statements about graphs.

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Cs6702 graph theory and applications lesson planappasami

This document contains a lesson plan for the subject "Graph Theory and Applications" taught to 8th semester Computer Science students. The lesson plan spans 14 weeks and covers 5 units: Introduction, Trees Connectivity and Planarity, Matrices Colouring and Directed Graph, Permutations and Combinations, and Generating Functions. It details the chapter topics to be covered in each class, the relevant textbook pages, and actual completion dates. Textbook references include Graph Theory by Narsingh Deo and Discrete and Combinatorial Mathematics by Grimaldi for the subject. The Head of Department and Principal are listed for sign-off on the lesson plan.

Computer organization-and-architecture-questions-and-answersappasami

The document discusses the basic functional units of a computer: - The input unit accepts coded data from devices like keyboards. - Memory stores programs and data, with primary storage operating at fast electronic speeds. - The arithmetic and logic unit (ALU) performs operations on data brought in from memory. - The output unit sends processed results outside the computer to devices like printers. - The control unit coordinates the other functional units and sequencing of operations.

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Cs6503 theory of computation may june 2016 be cse anna university question paper

1. Reg. No. : B.E. / B.Tech. DEGREE EXAMINATION, MAY / JUNE 2016 Fifth Semester Computer Science and Engineering CS6503 THEORY OF COMPUTATION (Regulation 2013) Time : Three hours Maximum : 100 marks Answer ALL Questions Part A – (𝟏𝟎 × 𝟐 = 𝟐𝟎 marks) 1. Draw a non-deterministic finite automata to accept strings containing the substring 0101. 2. State the pumping lemma for regular languages. 3. What do you mean by null production and unit production? Give an example.. 4. Construct a CFG fro set of strings that contain equal number of a‟s and b‟s over Σ={a, b}. 5. Does a Push down Automata have memory? Justify. 6. Define Push down Automata. 7. What are the differences between a Finite automata and a Turing machine? 8. What is Turing machine? 9. When is a Recursively Enumerable language said to be Recursive? 10. Identify whether „Tower of Hanoi‟ problem is tractable or intractable. Justify your answer. Part B – (5 × 𝟏𝟔 = 𝟖𝟎 marks) 11 (a) (i) Construct a NFA that accepts all strings hat end in 01. Give its transition table and extend transition function for the input string 00101. Also construct a DFA for the above NFA using subset construction method. (10) (ii) Prove the following by principle of induction. 𝑥2𝑛 𝑥=1 = 𝑛 𝑛+1 (2𝑛+1) 6 . (6) Or (b) (i) What is Regular Expression? Write a regular expression for set of strings that consists of alternating 0‟s and 1‟s. (8) (ii) Write and explain the algorithm for minimization of a DFA. Using the above algorithm minimize the following DFA. (8) A 0 1start B C D 0 1 0 E 1 1 F G D 0 0 01 1 1 1 0 0 Question Paper Code : 57255

2. 12 (a) (i) Construct a reduced grammar equivalent to the grammar G = (N, T, P, S) where, N = {S, A, C, D, E} (6) T = {a, b} P = { S → aAa, A → Sb, A → bCC, A → DaA, C → abb, C → DD, E → aC, D → aDA}. (ii) When is a grammar said to be ambiguous? Explain with the help of example. (5) (iii) Show the derivation steps and construct derivation tree for the string „ababbb‟. (5) by using left most derivation with the grammar. S → AB | ε A→ aB B→ Sb Or (b) (i) What is the purpose of normalization? Construct the CNF and GNF for the following grammar and explain the steps. (10) S → aAa | bBb | ε A→ C | a B→ C | b C→ CDE | ε D→ A | B | ab (ii) Construct a CFG for the regular expression (011+1) (01). (6) 13 (a) (i) Construct a Push down Automata to accept the following language L on Σ={a, b} by empty stack. 𝐿 = {𝑤𝑤R | 𝑤 ∈ 𝛴+ }. (10) (ii) What is an instantaneous description that the PDA? How will you represent it? Also give three important principles of ID and their transactions. (6) Or (b) (i) Explain acceptance by final state and acceptance by empty stack of a Push down Automata. (8) (ii) State the pumping lemma for CFL. Use pumping lemma to show that the language 𝐿 = {𝑎i 𝑏j 𝑐k | 𝑖 < 𝑗 < 𝑘} is not a CFL. (8) 14 (a) (i) Construct a Turing Machine to accept palindromes in an alphabet set Σ={a, b}. Trace the string “abab” and “baab”. (8) (ii) Explain the variations of Turing Machine. (8) Or (b) (i) Explain Halting problem. Is it solvable or unsolvable problem? Discuss. (8) (ii) Describe the Chomsky hierarchy of languages with example. What are the devices that accept these languages? (8) 15 (a) What is Universal Turing Machine? Bring out its significance. Also construct a Turing Machine to add two numbers and encode it. (16) Or (b) What is post correspondence problem (PCP)? Explain with the help of an example. (16) All the Best – No substitute for hard work. Mr. G. Appasami SET, NET, GATE, M.Sc., M.C.A., M.Phil., M.Tech., (P.hd.), MISTE, MIETE, AMIE, MCSI, MIAE, MIACSIT, MASCAP, MIARCS, MISIAM, MISCE, MIMS, MISCA, MISAET, PGDTS, PGDBA, PGDHN, PGDST, (AP / CSE / DRPEC).

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