# (a) R=01[((10)*+111)*+0]*1 (b) ((01+10)*00)*. [8+8] 4. (a) Find the left most and right most derivations for the word abba in the grammar

Size: px
Start display at page:

Download "(a) R=01[((10)*+111)*+0]*1 (b) ((01+10)*00)*. [8+8] 4. (a) Find the left most and right most derivations for the word abba in the grammar"

Transcription

1 Code No: R Set No. 1 III B.Tech I Semester Regular Examinations, November 2008 FORMAL LANGUAGES AND AUTOMATA THEORY (Computer Science & Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) Define NFA and explain with an example. (b) Conclude what type of strings will be accepted by the below Finite automata as shown in figure 1b. [6+10] Figure 1b 2. (a) Design a Moore Machine to determine the residue mod 4 for each binary string treated as integer. (b) Design a Mealy machine that uses its state to remember the last symbol read and emits output y whenever current input matches to previous one, and emits n otherwise. [8+8] 3. Construct an NFA for the following: (a) R=01[((10)*+111)*+0]*1 (b) ((01+10)*00)*. [8+8] 4. (a) Find the left most and right most derivations for the word abba in the grammar S AA A ab B bb/ (b) Write a CFG for EVEN and ODD palindromes. [2 8] 5. (a) Explain Chomsky hierarchy. (b) Construct PDA for set of all strings of balanced parenthesis. [8+8] 6. (a) Let G be the grammar given by S aabb/aaa, A abb/a, B bbb/a Construct the PDA that accepts the language generated by this grammar G. (b) Define Deterministic pushdown automata. Explain with an example. [8+8] 1 of 2

2 Code No: R Set No (a) Define a Turing machine mathematically. Define the term move in a TM. (b) Design a TM that recognizes the set {0 2n 1 n n = 0 }. [16] 8. Discuss: (a) The Hierarchy theorem. (b) LR(0) grammar. (c) Universal Turing Machine. [6+5+5] 2 of 2

3 Code No: R Set No. 2 III B.Tech I Semester Regular Examinations, November 2008 FORMAL LANGUAGES AND AUTOMATA THEORY (Computer Science & Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) Consider below transition (diagram 1a) and verify whether the following Strings will be accepted or not? Explain. Figure 1a i ii iii iv [8+8] (b) Design a DFA, M that accepts the language. L(M) = {w/w {a,b} * } and w does not contain 3 consecutive b s. 2. Construct DFA for given (figure 2) NFA with -moves. [16] Figure 2 3. Find a Regular expression corresponding to each of the following subsets over {0,1}*. (a) The set of all strings containing no three consecutive 0 s. (b) The set of all strings where the 10 th symbol from right end is a 1. 1 of 2

4 Code No: R Set No. 2 (c) The set of all strings over {0,1} having even number of 0 s & odd number of 1 s. (d) The set of all strings over {0,1} in which the number of occurrences of is divisible by 3. [4 4] 4. (a) Obtain a right linear grammar for the following FA as shown in figure 4a. Figure 4a (b) Obtain a left linear grammar for the above FA. [2 8] 5. (a) Prove that the following language is not context-free language L 1 = {a n b n c j/ n j 2n} (b) Simplify the following grammar: S AB A a B C B b C D D E. [8+8] 6. (a) Construct the PDA corresponding to the grammar: S aabb/aaa A abb/a B bbb/a. (b) Construct a PDA that accepts the language L = {wcw R /w {a, b} }. [8+8] 7. (a) Briefly explain the properties of recursive enumerable languages. (b) Design Turing machine to recognize the palindromes of digits {0,1}. Give its state transition diagram also. [8+8] 8. Give LR(0) items for the grammar S S, S asa/bsb/c. Find its equivalent DFA. Check the parsing by taking a suitable string. [16] 2 of 2

5 Code No: R Set No. 3 III B.Tech I Semester Regular Examinations, November 2008 FORMAL LANGUAGES AND AUTOMATA THEORY (Computer Science & Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) Design DFA to accept strings with c and d such that number d s are divisible by 4 (b) Design DFA which accepts language L ={ 0,000,00000,...} over {0}. [8+8] 2. For the following NFA with -moves convert it in to an NFA with out -moves and show that NFA with -moves accepts the same language as shown in figure 2. [16] 3. Consider the two regular expressions r=0*+1*, s=01*10*+1*0+(0*1)* Figure 2 (a) Find a string corresponding to r but not to s. (b) Find a string corresponding to s but not to r. [8+8] 4. Construct DFA for the following Regular expression ( ( a U b)* ( b U a)*)*. [16] 5. (a) When is a grammar is said to be in reduced form. (b) Convert the following grammar to GNF: G = ({A 1, A 2, A 3 }, {a, b}, P1, A1) Where P consists of the following: A 1 A 2 A 3 A 2 A 3 A 1 /b A 3 A 1 A 2 /a. [8+8] 6. (a) Define PDA. In what ways a PDA can show the acceptance of a string. Explain with examples. (b) Construct the PDA M for the language L={ww R /w {a, b} } such that L=L(M). [8+8] 1 of 2

6 Code No: R Set No (a) Let T be the Turing machine defined by the five tuples: (q 0, 0, q 1, 1, R), (q 0, 1, q 1, 0, r), (q 0, B, q 1, 0, R), (q 1, 0, q 2 1, L), (q 1, 1, q 1, 0, r)(q 1, B, q 2, 0, L). for each of the following initial tapes, determine the final tape when T halts, assuming that T begins in initial position. (b) Design a Turing machine to add two given integers. [8+8] 8. (a) Write a type 2 grammar with productions that generate the language. L={0 n 1 n /n >= 0} (b) Write short notes on linear bound automata. [8+8] 2 of 2

7 Code No: R Set No. 4 III B.Tech I Semester Regular Examinations, November 2008 FORMAL LANGUAGES AND AUTOMATA THEORY (Computer Science & Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Out of the following languages, which are/is accepted by given FA and explain as shown in figure 1. Figure 1 (a) (a+b)* (c+d)* (ef)* (b) (ab)* (cd)* (ef)* (c) (a+b)*+(c+d)*+(ef)* (d) ( (ab)*+ (cd)*+ (ef)* ) *. [4 4] 2. (a) Show that the FA are equivalent as shown in figure 2a. Figure 2a (b) Construct DFA for given FA as shown in figure 2b. [8+8] 1 of 2

8 Code No: R Set No. 4 Figure 2b 3. Give a regular expression for the following language L = {x {0, 1} x ends with 1 and does not contain the sub string 00}. [16] 4. (a) Construct DFA for the following regular expression ( ab U aba)*a (b) Write recursive definition of regular expression? [12+4] 5. (a) Show that L = {a i b j /j = i 2 } is not context free language. (b) List the properties of CFLs. (c) Find if the given grammar is finite or infinite. S AB, A BC/a, B CC/b, C a. [8+5+3] 6. (a) Find the PDA with only one state that accepts the language {a m b n : n > m } (b) Construct the PDA that recognizes the languages L={x= R : x {a,b} + }. [8+8] 7. (a) Design A Turing machine that accepts L = {a n b n n 0 } (b) What does the Turing Machine described by the 5-tules (q 0, 0, q 0 R), (q 0, 1, q 1, 0, r), (q 0, B, q 2, B, R), (q 1, 0, q 1, 0, R), (q 1, 1, q 0, 1, R) and (q 1, B, q 2, B, R) do when given a bit string as input? [8+8] 8. Write short notes on: (a) Church s hypothesis. (b) Ogden s lemma. (c) DPDA. [6+5+5] 2 of 2

### Skyup's Media. PART-B 2) Construct a Mealy machine which is equivalent to the Moore machine given in table.

Code No: XXXXX JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY, HYDERABAD B.Tech II Year I Semester Examinations (Common to CSE and IT) Note: This question paper contains two parts A and B. Part A is compulsory

More information

### R10 SET a) Construct a DFA that accepts an identifier of a C programming language. b) Differentiate between NFA and DFA?

R1 SET - 1 1. a) Construct a DFA that accepts an identifier of a C programming language. b) Differentiate between NFA and DFA? 2. a) Design a DFA that accepts the language over = {, 1} of all strings that

More information

### JNTUWORLD. Code No: R

Code No: R09220504 R09 SET-1 B.Tech II Year - II Semester Examinations, April-May, 2012 FORMAL LANGUAGES AND AUTOMATA THEORY (Computer Science and Engineering) Time: 3 hours Max. Marks: 75 Answer any five

More information

### T.E. (Computer Engineering) (Semester I) Examination, 2013 THEORY OF COMPUTATION (2008 Course)

*4459255* [4459] 255 Seat No. T.E. (Computer Engineering) (Semester I) Examination, 2013 THEY OF COMPUTATION (2008 Course) Time : 3 Hours Max. Marks : 100 Instructions : 1) Answers to the two Sections

More information

### Multiple Choice Questions

Techno India Batanagar Computer Science and Engineering Model Questions Subject Name: Formal Language and Automata Theory Subject Code: CS 402 Multiple Choice Questions 1. The basic limitation of an FSM

More information

### CT32 COMPUTER NETWORKS DEC 2015

Q.2 a. Using the principle of mathematical induction, prove that (10 (2n-1) +1) is divisible by 11 for all n N (8) Let P(n): (10 (2n-1) +1) is divisible by 11 For n = 1, the given expression becomes (10

More information

### UNIT I PART A PART B

OXFORD ENGINEERING COLLEGE (NAAC ACCREDITED WITH B GRADE) DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING LIST OF QUESTIONS YEAR/SEM: III/V STAFF NAME: Dr. Sangeetha Senthilkumar SUB.CODE: CS6503 SUB.NAME:

More information

VALLIAMMAI ENGNIEERING COLLEGE SRM Nagar, Kattankulathur 603203. DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING Year & Semester : III Year, V Semester Section : CSE - 1 & 2 Subject Code : CS6503 Subject

More information

### QUESTION BANK. Formal Languages and Automata Theory(10CS56)

QUESTION BANK Formal Languages and Automata Theory(10CS56) Chapter 1 1. Define the following terms & explain with examples. i) Grammar ii) Language 2. Mention the difference between DFA, NFA and εnfa.

More information

### Theory of Computation, Homework 3 Sample Solution

Theory of Computation, Homework 3 Sample Solution 3.8 b.) The following machine M will do: M = "On input string : 1. Scan the tape and mark the first 1 which has not been marked. If no unmarked 1 is found,

More information

### Finite Automata Theory and Formal Languages TMV027/DIT321 LP4 2016

Finite Automata Theory and Formal Languages TMV027/DIT321 LP4 2016 Lecture 15 Ana Bove May 23rd 2016 More on Turing machines; Summary of the course. Overview of today s lecture: Recap: PDA, TM Push-down

More information

### Decidable Problems. We examine the problems for which there is an algorithm.

Decidable Problems We examine the problems for which there is an algorithm. Decidable Problems A problem asks a yes/no question about some input. The problem is decidable if there is a program that always

More information

### CS/B.Tech/CSE/IT/EVEN/SEM-4/CS-402/ ItIauIafIaAblll~AladUnrtel1ity

CS/B.Tech/CSE/IT/EVEN/SEM-4/CS-402/2015-16 ItIauIafIaAblll~AladUnrtel1ity ~ t; ~~ ) MAULANA ABUL KALAM AZAD UNIVERSITY OF TECHNOLOGY, WEST BENGAL Paper Code: CS-402 FORMAL LANGUAGE AND AUTOMATA THEORY

More information

### CS210 THEORY OF COMPUTATION QUESTION BANK PART -A UNIT- I

CS210 THEORY OF COMPUTATION QUESTION BANK PART -A UNIT- I 1) Is it true that the language accepted by any NDFA is different from the regular language? Justify your answer. 2) Describe the following sets

More information

### CS5371 Theory of Computation. Lecture 8: Automata Theory VI (PDA, PDA = CFG)

CS5371 Theory of Computation Lecture 8: Automata Theory VI (PDA, PDA = CFG) Objectives Introduce Pushdown Automaton (PDA) Show that PDA = CFG In terms of descriptive power Pushdown Automaton (PDA) Roughly

More information

### CS 44 Exam #2 February 14, 2001

CS 44 Exam #2 February 14, 2001 Name Time Started: Time Finished: Each question is equally weighted. You may omit two questions, but you must answer #8, and you can only omit one of #6 or #7. Circle the

More information

### Outline. Language Hierarchy

Outline Language Hierarchy Definition of Turing Machine TM Variants and Equivalence Decidability Reducibility Language Hierarchy Regular: finite memory CFG/PDA: infinite memory but in stack space TM: infinite

More information

### Computer Sciences Department

1 Reference Book: INTRODUCTION TO THE THEORY OF COMPUTATION, SECOND EDITION, by: MICHAEL SIPSER 3 D E C I D A B I L I T Y 4 Objectives 5 Objectives investigate the power of algorithms to solve problems.

More information

### R10 SET a) Explain the Architecture of 8085 Microprocessor? b) Explain instruction set Architecture Design?

Code No: R22054 COMPUTER ORGANIZATION (Com. to CSE, ECC) 1. a) Explain the Architecture of 8085 Microprocessor? b) Explain instruction set Architecture Design? 2. Explain Memory Subsystem Organization

More information

### TAFL 1 (ECS-403) Unit- V. 5.1 Turing Machine. 5.2 TM as computer of Integer Function

TAFL 1 (ECS-403) Unit- V 5.1 Turing Machine 5.2 TM as computer of Integer Function 5.2.1 Simulating Turing Machine by Computer 5.2.2 Simulating Computer by Turing Machine 5.3 Universal Turing Machine 5.4

More information

### CS402 Theory of Automata Solved Subjective From Midterm Papers. MIDTERM SPRING 2012 CS402 Theory of Automata

Solved Subjective From Midterm Papers Dec 07,2012 MC100401285 Moaaz.pk@gmail.com Mc100401285@gmail.com PSMD01 MIDTERM SPRING 2012 Q. Point of Kleen Theory. Answer:- (Page 25) 1. If a language can be accepted

More information

### QUESTION BANK. Unit 1. Introduction to Finite Automata

QUESTION BANK Unit 1 Introduction to Finite Automata 1. Obtain DFAs to accept strings of a s and b s having exactly one a.(5m )(Jun-Jul 10) 2. Obtain a DFA to accept strings of a s and b s having even

More information

### Finite Automata. Dr. Nadeem Akhtar. Assistant Professor Department of Computer Science & IT The Islamia University of Bahawalpur

Finite Automata Dr. Nadeem Akhtar Assistant Professor Department of Computer Science & IT The Islamia University of Bahawalpur PhD Laboratory IRISA-UBS University of South Brittany European University

More information

### AUBER (Models of Computation, Languages and Automata) EXERCISES

AUBER (Models of Computation, Languages and Automata) EXERCISES Xavier Vera, 2002 Languages and alphabets 1.1 Let be an alphabet, and λ the empty string over. (i) Is λ in? (ii) Is it true that λλλ=λ? Is

More information

### University of Nevada, Las Vegas Computer Science 456/656 Fall 2016

University of Nevada, Las Vegas Computer Science 456/656 Fall 2016 The entire examination is 925 points. The real final will be much shorter. Name: No books, notes, scratch paper, or calculators. Use pen

More information

### DHANALAKSHMI SRINIVASAN INSTITUTE OF RESEARCH AND TECHNOLOGY SIRUVACHUR, PERAMBALUR DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING

DHANALAKSHMI SRINIVASAN INSTITUTE OF RESEARCH AND TECHNOLOGY SIRUVACHUR, PERAMBALUR-621113 DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING Third Year CSE( Sem:V) CS2303- THEORY OF COMPUTATION PART B-16

More information

### Theory of Programming Languages COMP360

Theory of Programming Languages COMP360 Sometimes it is the people no one imagines anything of, who do the things that no one can imagine Alan Turing What can be computed? Before people even built computers,

More information

### 1. Which of the following regular expressions over {0, 1} denotes the set of all strings not containing 100 as a sub-string?

Multiple choice type questions. Which of the following regular expressions over {, } denotes the set of all strings not containing as a sub-string? 2. DFA has a) *(*)* b) ** c) ** d) *(+)* a) single final

More information

### Actually talking about Turing machines this time

Actually talking about Turing machines this time 10/25/17 (Using slides adapted from the book) Administrivia HW due now (Pumping lemma for context-free languages) HW due Friday (Building TMs) Exam 2 out

More information

### Answer All Questions. All Questions Carry Equal Marks. Time: 20 Min. Marks: 10.

Code No: 134BD Set No. 1 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech. II Year II Sem., I Mid-Term Examinations, February - 2018 FORMAL LANGUAGES AND AUTOMATA THEORY Objective Exam Name:

More information

### Learn Smart and Grow with world

Learn Smart and Grow with world All Department Smart Study Materials Available Smartkalvi.com TABLE OF CONTENTS S.No DATE TOPIC PAGE NO. UNIT-I FINITE AUTOMATA 1 Introduction 1 2 Basic Mathematical Notation

More information

### The Turing Machine. Unsolvable Problems. Undecidability. The Church-Turing Thesis (1936) Decision Problem. Decision Problems

The Turing Machine Unsolvable Problems Motivating idea Build a theoretical a human computer Likened to a human with a paper and pencil that can solve problems in an algorithmic way The theoretical machine

More information

### TOPIC PAGE NO. UNIT-I FINITE AUTOMATA

TABLE OF CONTENTS SNo DATE TOPIC PAGE NO UNIT-I FINITE AUTOMATA 1 Introduction 1 2 Basic Mathematical Notation Techniques 3 3 Finite State systems 4 4 Basic Definitions 6 5 Finite Automaton 7 6 DFA NDFA

More information

### Ambiguous Grammars and Compactification

Ambiguous Grammars and Compactification Mridul Aanjaneya Stanford University July 17, 2012 Mridul Aanjaneya Automata Theory 1/ 44 Midterm Review Mathematical Induction and Pigeonhole Principle Finite Automata

More information

### Turing Machines. A transducer is a finite state machine (FST) whose output is a string and not just accept or reject.

Turing Machines Transducers: A transducer is a finite state machine (FST) whose output is a string and not just accept or reject. Each transition of an FST is labeled with two symbols, one designating

More information

### ONE-STACK AUTOMATA AS ACCEPTORS OF CONTEXT-FREE LANGUAGES *

ONE-STACK AUTOMATA AS ACCEPTORS OF CONTEXT-FREE LANGUAGES * Pradip Peter Dey, Mohammad Amin, Bhaskar Raj Sinha and Alireza Farahani National University 3678 Aero Court San Diego, CA 92123 {pdey, mamin,

More information

### Automata Theory CS S-FR Final Review

Automata Theory CS411-2015S-FR Final Review David Galles Department of Computer Science University of San Francisco FR-0: Sets & Functions Sets Membership: a?{a,b,c} a?{b,c} a?{b,{a,b,c},d} {a,b,c}?{b,{a,b,c},d}

More information

### Final Course Review. Reading: Chapters 1-9

Final Course Review Reading: Chapters 1-9 1 Objectives Introduce concepts in automata theory and theory of computation Identify different formal language classes and their relationships Design grammars

More information

### CSC-461 Exam #2 April 16, 2014

Pledge: On my honor, I pledge that I have not discussed any of the questions on this exam with fellow students, nor will I until after 7 p.m. tonight. Signed: CSC-461 Exam #2 April 16, 2014 Name Time Started:

More information

### Introduction to Computers & Programming

16.070 Introduction to Computers & Programming Theory of computation 5: Reducibility, Turing machines Prof. Kristina Lundqvist Dept. of Aero/Astro, MIT States and transition function State control A finite

More information

### PDA s. and Formal Languages. Automata Theory CS 573. Outline of equivalence of PDA s and CFG s. (see Theorem 5.3)

CS 573 Automata Theory and Formal Languages Professor Leslie Lander Lecture # 20 November 13, 2000 Greibach Normal Form (GNF) Sheila Greibach s normal form (GNF) for a CFG is one where EVERY production

More information

### AUTOMATA THEORY AND COMPUTABILITY

AUTOMATA THEORY AND COMPUTABILITY QUESTION BANK Module 1 : Introduction to theory of computation and FSM Objective: Upon the completion of this chapter you will be able to Define Finite automata, Basic

More information

### CSE 105 THEORY OF COMPUTATION

CSE 105 THEORY OF COMPUTATION Fall 2016 http://cseweb.ucsd.edu/classes/fa16/cse105-abc/ Today's learning goals Sipser sec 3.2 Describe several variants of Turing machines and informally explain why they

More information

### 1. [5 points each] True or False. If the question is currently open, write O or Open.

University of Nevada, Las Vegas Computer Science 456/656 Spring 2018 Practice for the Final on May 9, 2018 The entire examination is 775 points. The real final will be much shorter. Name: No books, notes,

More information

### Limitations of Algorithmic Solvability In this Chapter we investigate the power of algorithms to solve problems Some can be solved algorithmically and

Computer Language Theory Chapter 4: Decidability 1 Limitations of Algorithmic Solvability In this Chapter we investigate the power of algorithms to solve problems Some can be solved algorithmically and

More information

### Regular Languages (14 points) Solution: Problem 1 (6 points) Minimize the following automaton M. Show that the resulting DFA is minimal.

Regular Languages (14 points) Problem 1 (6 points) inimize the following automaton Show that the resulting DFA is minimal. Solution: We apply the State Reduction by Set Partitioning algorithm (särskiljandealgoritmen)

More information

### Derivations of a CFG. MACM 300 Formal Languages and Automata. Context-free Grammars. Derivations and parse trees

Derivations of a CFG MACM 300 Formal Languages and Automata Anoop Sarkar http://www.cs.sfu.ca/~anoop strings grow on trees strings grow on Noun strings grow Object strings Verb Object Noun Verb Object

More information

### ECS 120 Lesson 16 Turing Machines, Pt. 2

ECS 120 Lesson 16 Turing Machines, Pt. 2 Oliver Kreylos Friday, May 4th, 2001 In the last lesson, we looked at Turing Machines, their differences to finite state machines and pushdown automata, and their

More information

### The Big Picture. Chapter 3

The Big Picture Chapter 3 Examining Computational Problems We want to examine a given computational problem and see how difficult it is. Then we need to compare problems Problems appear different We want

More information

### Closure Properties of CFLs; Introducing TMs. CS154 Chris Pollett Apr 9, 2007.

Closure Properties of CFLs; Introducing TMs CS154 Chris Pollett Apr 9, 2007. Outline Closure Properties of Context Free Languages Algorithms for CFLs Introducing Turing Machines Closure Properties of CFL

More information

### I have read and understand all of the instructions below, and I will obey the Academic Honor Code.

Midterm Exam CS 341-451: Foundations of Computer Science II Fall 2014, elearning section Prof. Marvin K. Nakayama Print family (or last) name: Print given (or first) name: I have read and understand all

More information

### Theory of Computation

Theory of Computation For Computer Science & Information Technology By www.thegateacademy.com Syllabus Syllabus for Theory of Computation Regular Expressions and Finite Automata, Context-Free Grammar s

More information

### CSE 105 THEORY OF COMPUTATION

CSE 105 THEORY OF COMPUTATION Spring 2016 http://cseweb.ucsd.edu/classes/sp16/cse105-ab/ Today's learning goals Sipser Ch 3.2, 3.3 Define variants of TMs Enumerators Multi-tape TMs Nondeterministic TMs

More information

### Chapter 14: Pushdown Automata

Chapter 14: Pushdown Automata Peter Cappello Department of Computer Science University of California, Santa Barbara Santa Barbara, CA 93106 cappello@cs.ucsb.edu The corresponding textbook chapter should

More information

### Formal Grammars and Abstract Machines. Sahar Al Seesi

Formal Grammars and Abstract Machines Sahar Al Seesi What are Formal Languages Describing the sentence structure of a language in a formal way Used in Natural Language Processing Applications (translators,

More information

### Formal Languages and Automata

Mobile Computing and Software Engineering p. 1/3 Formal Languages and Automata Chapter 3 Regular languages and Regular Grammars Chuan-Ming Liu cmliu@csie.ntut.edu.tw Department of Computer Science and

More information

### CISC 4090 Theory of Computation

CISC 4090 Theory of Computation Turing machines Professor Daniel Leeds dleeds@fordham.edu JMH 332 Alan Turing (1912-1954) Father of Theoretical Computer Science Key figure in Artificial Intelligence Codebreaker

More information

### CS402 - Theory of Automata Glossary By

CS402 - Theory of Automata Glossary By Acyclic Graph : A directed graph is said to be acyclic if it contains no cycles. Algorithm : A detailed and unambiguous sequence of instructions that describes how

More information

### Theory of Computations Spring 2016 Practice Final Exam Solutions

1 of 8 Theory of Computations Spring 2016 Practice Final Exam Solutions Name: Directions: Answer the questions as well as you can. Partial credit will be given, so show your work where appropriate. Try

More information

### Source of Slides: Introduction to Automata Theory, Languages, and Computation By John E. Hopcroft, Rajeev Motwani and Jeffrey D.

Source of Slides: Introduction to Automata Theory, Languages, and Computation By John E. Hopcroft, Rajeev Motwani and Jeffrey D. Ullman And Introduction to Languages and The by J. C. Martin Basic Mathematical

More information

### Turing Machine Languages

Turing Machine Languages Based on Chapters 23-24-25 of (Cohen 1997) Introduction A language L over alphabet is called recursively enumerable (r.e.) if there is a Turing Machine T that accepts every word

More information

### CS21 Decidability and Tractability

CS21 Decidability and Tractability Lecture 9 January 26, 2018 Outline Turing Machines and variants multitape TMs nondeterministic TMs Church-Turing Thesis decidable, RE, co-re languages Deciding and Recognizing

More information

### 6 NFA and Regular Expressions

Formal Language and Automata Theory: CS21004 6 NFA and Regular Expressions 6.1 Nondeterministic Finite Automata A nondeterministic finite automata (NFA) is a 5-tuple where 1. is a finite set of states

More information

### Universal Turing Machine Chomsky Hierarchy Decidability Reducibility Uncomputable Functions Rice s Theorem Decidability Continued

CD5080 AUBER odels of Computation, anguages and Automata ecture 14 älardalen University Content Universal Turing achine Chomsky Hierarchy Decidability Reducibility Uncomputable Functions Rice s Decidability

More information

### Decision Properties for Context-free Languages

Previously: Decision Properties for Context-free Languages CMPU 240 Language Theory and Computation Fall 2018 Context-free languages Pumping Lemma for CFLs Closure properties for CFLs Today: Assignment

More information

### 1. Draw the state graphs for the finite automata which accept sets of strings composed of zeros and ones which:

P R O B L E M S Finite Autom ata. Draw the state graphs for the finite automata which accept sets of strings composed of zeros and ones which: a) Are a multiple of three in length. b) End with the string

More information

### Theory of Computation Dr. Weiss Extra Practice Exam Solutions

Name: of 7 Theory of Computation Dr. Weiss Extra Practice Exam Solutions Directions: Answer the questions as well as you can. Partial credit will be given, so show your work where appropriate. Try to be

More information

### LECTURE NOTES THEORY OF COMPUTATION

LECTURE NOTES ON THEORY OF COMPUTATION P Anjaiah Assistant Professor Ms. B Ramyasree Assistant Professor Ms. E Umashankari Assistant Professor Ms. A Jayanthi Assistant Professor INSTITUTE OF AERONAUTICAL

More information

### Last lecture CMSC330. This lecture. Finite Automata: States. Finite Automata. Implementing Regular Expressions. Languages. Regular expressions

Last lecture CMSC330 Finite Automata Languages Sets of strings Operations on languages Regular expressions Constants Operators Precedence 1 2 Finite automata States Transitions Examples Types This lecture

More information

### Languages and Automata

Languages and Automata What are the Big Ideas? Tuesday, August 30, 2011 Reading: Sipser 0.1 CS235 Languages and Automata Department of Computer Science Wellesley College Why Take CS235? 1. It s required

More information

### Theory Bridge Exam Example Questions Version of June 6, 2008

Theory Bridge Exam Example Questions Version of June 6, 2008 This is a collection of sample theory bridge exam questions. This is just to get some idea of the format of the bridge exam and the level of

More information

### Automata Theory TEST 1 Answers Max points: 156 Grade basis: 150 Median grade: 81%

Automata Theory TEST 1 Answers Max points: 156 Grade basis: 150 Median grade: 81% 1. (2 pts) See text. You can t be sloppy defining terms like this. You must show a bijection between the natural numbers

More information

### LECTURE NOTES THEORY OF COMPUTATION

LECTURE NOTES ON THEORY OF COMPUTATION Dr. K Rajendra Prasad Professor Ms. N Mamtha Assistant Professor Ms. S Swarajya Lakshmi Assistant Professor Mr. D Abdulla Assistant Professor INSTITUTE OF AERONAUTICAL

More information

### Midterm Exam II CIS 341: Foundations of Computer Science II Spring 2006, day section Prof. Marvin K. Nakayama

Midterm Exam II CIS 341: Foundations of Computer Science II Spring 2006, day section Prof. Marvin K. Nakayama Print family (or last) name: Print given (or first) name: I have read and understand all of

More information

### CS402 - Theory of Automata FAQs By

CS402 - Theory of Automata FAQs By Define the main formula of Regular expressions? Define the back ground of regular expression? Regular expressions are a notation that you can think of similar to a programming

More information

### (DMTCS 01) Answer Question No.1 is compulsory (15) Answer One question from each unit (4 15=60) 1) a) State whether the following is True/False:

(DMTCS 01) M.Tech. DEGREE EXAMINATION, DECEMBER - 2015 (Examination at the end of First Year) COMPUTER SCIENCE Paper - I : Data structures Time : 03 Hours Maximum Marks : 75 Answer Question No.1 is compulsory

More information

### An Interactive Approach to Formal Languages and Automata with JFLAP

An Interactive Approach to Formal Languages and Automata with JFLAP Susan H. Rodger Duke University NSF CCLI Showcase March 9, 2007 Supported by NSF Grant DUE 0442513. Outline Overview of JFLAP Examples

More information

### Theory of Computations Spring 2016 Practice Final

1 of 6 Theory of Computations Spring 2016 Practice Final 1. True/False questions: For each part, circle either True or False. (23 points: 1 points each) a. A TM can compute anything a desktop PC can, although

More information

### Theory and Compiling COMP360

Theory and Compiling COMP360 It has been said that man is a rational animal. All my life I have been searching for evidence which could support this. Bertrand Russell Reading Read sections 2.1 3.2 in the

More information

### Formal languages and computation models

Formal languages and computation models Guy Perrier Bibliography John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman - Introduction to Automata Theory, Languages, and Computation - Addison Wesley, 2006.

More information

### 1. (a) What are the closure properties of Regular sets? Explain. (b) Briefly explain the logical phases of a compiler model. [8+8]

Code No: R05311201 Set No. 1 1. (a) What are the closure properties of Regular sets? Explain. (b) Briefly explain the logical phases of a compiler model. [8+8] 2. Compute the FIRST and FOLLOW sets of each

More information

### Finite Automata Theory and Formal Languages TMV027/DIT321 LP4 2018

Finite Automata Theory and Formal Languages TMV027/DIT321 LP4 2018 Lecture 11 Ana Bove April 26th 2018 Recap: Regular Languages Decision properties of RL: Is it empty? Does it contain this word? Contains

More information

### M.Sc. (Computer Science) I Year Assignments for May Paper I DATA STRUCTURES Assignment I

Paper I DATA STRUCTURES (DMCS 01) 1. Explain in detail about the overview of Data structures. 2. Explain circular linked list and double-linked list. 3. Explain CPU scheduling in Multiprogramming Environment.

More information

### THEORY OF COMPUTATION

THEORY OF COMPUTATION UNIT-1 INTRODUCTION Overview This chapter begins with an overview of those areas in the theory of computation that are basic foundation of learning TOC. This unit covers the introduction

More information

### CpSc 421 Final Solutions

CpSc 421 Final Solutions Do any eight of the ten problems below. If you attempt more than eight problems, please indicate which ones to grade (otherwise we will make a random choice). This allows you to

More information

### Languages and Compilers

Principles of Software Engineering and Operational Systems Languages and Compilers SDAGE: Level I 2012-13 3. Formal Languages, Grammars and Automata Dr Valery Adzhiev vadzhiev@bournemouth.ac.uk Office:

More information

### Pushdown Automata. A PDA is an FA together with a stack.

Pushdown Automata A PDA is an FA together with a stack. Stacks A stack stores information on the last-in firstout principle. Items are added on top by pushing; items are removed from the top by popping.

More information

### Name: Finite Automata

Unit No: I Name: Finite Automata What is TOC? In theoretical computer science, the theory of computation is the branch that deals with whether and how efficiently problems can be solved on a model of computation,

More information

### Definition 2.8: A CFG is in Chomsky normal form if every rule. only appear on the left-hand side, we allow the rule S ǫ.

CS533 Class 02b: 1 c P. Heeman, 2017 CNF Pushdown Automata Definition Equivalence Overview CS533 Class 02b: 2 c P. Heeman, 2017 Chomsky Normal Form Definition 2.8: A CFG is in Chomsky normal form if every

More information

### CSE 105 THEORY OF COMPUTATION

CSE 105 THEORY OF COMPUTATION Spring 2017 http://cseweb.ucsd.edu/classes/sp17/cse105-ab/ Today's learning goals Sipser Ch 1.2, 1.3 Decide whether or not a string is described by a given regular expression

More information

### Enumerations and Turing Machines

Enumerations and Turing Machines Mridul Aanjaneya Stanford University August 07, 2012 Mridul Aanjaneya Automata Theory 1/ 35 Finite Sets Intuitively, a finite set is a set for which there is a particular

More information

### Total No. of Questions : 18] [Total No. of Pages : 02. M.Sc. DEGREE EXAMINATION, DEC First Year COMPUTER SCIENCE.

(DMCS01) Total No. of Questions : 18] [Total No. of Pages : 02 M.Sc. DEGREE EXAMINATION, DEC. 2016 First Year COMPUTER SCIENCE Data Structures Time : 3 Hours Maximum Marks : 70 Section - A (3 x 15 = 45)

More information

### UNIT 1 SNS COLLEGE OF ENGINEERING

1 SNS COLLEGE OF ENGINEERING DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING THEORY OF COMPUTATION TWO MARKS WITH ANSWERS UNIT 1 1. Define set. A set is a collection of objects. E.g.: The collection of

More information

### A Characterization of the Chomsky Hierarchy by String Turing Machines

A Characterization of the Chomsky Hierarchy by String Turing Machines Hans W. Lang University of Applied Sciences, Flensburg, Germany Abstract A string Turing machine is a variant of a Turing machine designed

More information

### A Note on the Succinctness of Descriptions of Deterministic Languages

INFORMATION AND CONTROL 32, 139-145 (1976) A Note on the Succinctness of Descriptions of Deterministic Languages LESLIE G. VALIANT Centre for Computer Studies, University of Leeds, Leeds, United Kingdom

More information

### Homework. Announcements. Before We Start. Languages. Plan for today. Chomsky Normal Form. Final Exam Dates have been announced

Homework Homework #3 returned Homework #4 due today Homework #5 Pg 169 -- Exercise 4 Pg 183 -- Exercise 4c,e,i Pg 184 -- Exercise 10 Pg 184 -- Exercise 12 Pg 185 -- Exercise 17 Due 10 / 17 Announcements

More information

### CSE 105 THEORY OF COMPUTATION

CSE 105 THEORY OF COMPUTATION Spring 2017 http://cseweb.ucsd.edu/classes/sp17/cse105-ab/ Today's learning goals Sipser Ch 2, 3.1 State and use the Church-Turing thesis. Describe several variants of Turing

More information

### Theory of Languages and Automata

Theory of Languages and Automata Chapter 3- The Church-Turing Thesis Sharif University of Technology Turing Machine O Several models of computing devices Finite automata Pushdown automata O Tasks that

More information

### ROEVER COLLEGE OF ENGINEERING AND TECHNOLOGY Elambalur, Perambalur DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING UNIT-I AUTOMATA

ROEVER COLLEGE OF ENGINEERING AND TECHNOLOGY Elambalur, Perambalur 621 220 DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING Year & Semester : III / V Subject Code : CS6503 Subject Name : Theory of Computation

More information

### (DCS/DIT311) Answer question no.1 compulsory (15 1 = 15) Answer ONE question for each unit (4 15 = 60) 1) Write short notes on :

(DCS/DIT311) B.Tech. DEGREE EXAMINATION, DEC. - 2013 (Examination at the end of Third Year Third Semester) Computer Science & IT Paper - I : OPERATING SYSTEMS Time : 3 Hours Maximum Marks : 75 Answer question

More information