CSE2001, Fall 2006
1
Assignment 5
Due: Wednesday, December 6, 12:00 pm Instructions
You may work on this assignment in pairs. Each pair should hand in a single set of solutions. The front page of you
CSE 2001: Introduction to Theory of Computation
Winter 2006
Next
Equivalence of PDAs, CFLs Non-CF languages CFL pumping lemma Closure properties of CFLs
Suprakash Datta
[email protected] Office: CSEB
CSE 2001: Introduction to Theory of Computation
Winter 2006
Next
Computability Turing machines TM-computable/recognizable languages Variants of TMs
Suprakash Datta
[email protected] Office: CSEB 3043
CSE 2001: Introduction to Theory of Computation
Winter 2006
Outline
Last class: Introduction to Turing machines TM-computable/recognizable languages Today: Recall the definition of TMs Variants of TMs
CSE 2001: Introduction to Theory of Computation
Winter 2006
Next
Towards undecidability: The Halting Problem Countable and uncountable infinities Diagonalization arguments
Suprakash Datta
[email protected]
COSC 2001: Introduction to the theory of computation Assignment 1 (Released January 18, 2006) Submission deadline: 6:45 pm, Jan 31, 2006
1. The assignment can be handwritten or typed. It MUST be legib
COSC 2001: Introduction to the theory of computation Assignment 2 (Released February 28, 2006) Submission deadline: 4 pm, Mar 15, 2006
1. The assignment can be handwritten or typed. It MUST be legible
COSC 2001: Introduction to the theory of computation Assignment 3 (Released March 23, 2006) Submission deadline: 4 pm, Apr 5, 2006
1. The assignment can be handwritten or typed. It MUST be legible. 2.
CSE2001, Fall 2006
1
Assignment 1
Due: Friday, September 22, 9:00 am Instructions
You may work on this assignment in pairs. Each pair should hand in a single set of solutions. The front page of your
CSE2001, Fall 2006
1
Assignment 2
Due: Friday, October 13, 9:00 am Instructions
You may work on this assignment in pairs. Each pair should hand in a single set of solutions. The front page of your so
CSE2001, Fall 2006
1
Assignment 3
Due: Friday, November 10, 12:00 pm Instructions
You may work on this assignment in pairs. Each pair should hand in a single set of solutions. The front page of your
CSE2001, Fall 2006
1
Assignment 4
Due: Monday, November 27, 5:30 pm Instructions
You may work on this assignment in pairs. Each pair should hand in a single set of solutions. The front page of your s
CSE 2001: Introduction to Theory of Computation
Winter 2006
Non-regular Languages 1.4
Which languages cannot be recognized by finite automata? Examples: L= cfw_0n1n | nN PAL = cfw_w | w = wR Playing
Q1b: Yes, concatenation of two regular languages.
Q2b: Equivalent (not equal) to complement of A_TM
Q2d: RE (Turing recognizable)
Q5: Yes. Remember i-j mod 5 in the states.
Q8: Use the construction us
1. Q 4.23 (solved in the book). Check your understanding by trying 4.24, 4.25
(same idea works here).
2. Q 4.27 - see if you can relate this to the hw problem on infinite CFLs.
3. Q 5.13
4. Q 3.19
5
Page 1 out of 8 YORK UNIVERSITY FACULTY OF PURE AND APPLIED SCIENCE 2005 WINTER TERM EXAMINATION Course Number: COSC2001 Title: Introduction to Theory of Computation Duration: 3 hours No aids allowed.
Practice problems:
1. Consider the alphabet cfw_a,b. Design a DFA for the language
L = cfw_w | |w|>0, and the difference in the number of a's and b's is even
2. Consider the alphabet cfw_a,b. Design
Nothing written on the back of this page will be marked
1
CSE2001 Introduction to the Theory of Computation, Fall 2006
Test 1
Monday, October 16, 2006 Duration 75 minutes No aids allowed Counting the
Nothing written on the back of this page will be marked
1
CSE2001 Introduction to the Theory of Computation, Fall 2006
Test 2
Monday, November 13, 2006 Duration 75 minutes No aids allowed Counting the
1. Prove that the language L = cfw_w | w=vuu^R, for u,v in Sigma^* is a CFL by constructing a CFG and a PDA.
2. Prove that the intersection of a CFL and a regular language is a CFL.
3. Problem 2.14
4.
Abstract Thinking, Intro to the Theory of Computation SC/COSC 2001 3.0 Lecture Notes
Je Edmonds Winter 99-00, Version 0.2
Contents
1 Preface 2 DFAs, Iterative Programs, and Loop Invariants 2.1 2.2 2.3
Q1b: Yes, concatenation of two regular languages.
Q2b: Equivalent (not equal) to complement of A_TM
Q2d: RE (Turing recognizable)
Q5: Yes. Remember i-j mod 5 in the states.
Q8: Use the construction us
CSE 2001: Introduction to Theory of Computation
Winter 2006
Administrivia
Lectures: Tue 7:00-10:00 pm (SLH E) Exams: 2 tests (40%), final (45%) Homework (15%): equally divided between 3 assignments. S
CSE 2001: Introduction to Theory of Computation
Winter 2006
Administrivia
Lectures: Tue 7:00-10:00 pm (SLH E) Exams: 2 tests (40%), final (45%) Homework (15%): equally divided between 3 assignments. S
http:/www.cse.yorku.ca/course/2001/review-hint.pdf Note: in the hint for question 17, the line "for all strings x of length i" should read "for all strings x of length at most i".