| Week | Date | Topic/Read Before Class | To be assigned | To be collected | |
| 1 | M, 09/04 | Labor day: no class | |||
| W, 09/06 | Course information, go over the syllabus,
Ch. 0 Introduction sets sequences |
Warm up | |||
| F, 09/08 | K-day: no class | ||||
| 2 | M, 09/11 |
Ch. 0 Introduction (cont'd)
functions total functions, one-to-one functions proof techniques proof by construction |
|||
| W, 09/13 |
Solve homework 1
Ch. 0 Introduction (cont'd) proof techniques proof by contradiction proof by induction Section 4.2 proof by diagonalization the set of even numbers is countable the set of odd numbers is countable the set of pairs is countable the set of real numbers is uncountable the power set of N is uncountable |
hw2: countability | hw1 | ||
| F, 9/15 |
Section 4.2
proof by diagonalization the set of pairs is countable the set of real numbers is uncountable the set of functions is uncountable the power set of N is uncountable |
||||
| 3 | M, 09/18 |
Section 4.2
proof by diagonalization the power set of N is uncountable the set of integers (positive and negative) is countable the set of repeating functions is uncountable |
|||
| W, 9/20 | Solve homework 2
Chapter 1: Finite Automata definition design accepting a string regular operations |
hw3: Ch. 1 | hw2 | ||
| F, 9/22 | Chapter 1: Finite Automata
regular operations Theorem 1.25 regular languages are closed under union |
||||
| 4 | M, 9/25 | Chapter 1: Finite Automata
NFAs converting NFAs to DFAs |
|||
| W, 9/27 | Solve homework 3
Chapter 1: Finite Automata regular languages are closed under union regular languages are closed under concatenation | hw4: Ch. 1 | hw3 | ||
| F, 9/29 | Chapter 1: Finite Automata
regular languages are closed under star regular expressions Theorem 1.54 A language is regular if some regular expression describes it |
||||
| 5 | M, 10/02 | Chapter 1: Finite Automata
Can prove a language is regular by constructing A DFA, an NFA, or a regular expression The pumping lemma for regular languages repeating states while processing a string the pumping lemma proving that 0n1n is not regular |
|||
| W, 10/04 | Solve homework 4
Chapter 1: Finite Automata The pumping lemma for regular languages proving that {w | w has an equal number of 0s and 1s} is not regular proving that {ww |w ∈ {0,1}*} is not regular |
hw5: Ch. 1,2 | hw4 | ||
| F, 10/06 | Chapter 1: Finite Automata
The pumping lemma for regular languages proving that {1n2 | n ≥ 0 } is not regular The big picture: wrap up puzzle ( jpg ) ( postscript ) Chapter 2: Context-Free Languages Context-free grammars |
||||
| 6 | M, 10/09 | Chapter 2: Context-Free Languages
Context-free grammars Parse trees Ambiguous grammars |
|||
| W, 10/11 | Chapter 2: Context-Free Languages
Chomsky normal form Pushdown automaton |
hw6: Ch. 2 | hw5 | ||
| F, 10/13 | Solve homework 5
Chapter 2: Context-Free Languages Pushdown automaton examples |
||||
| 7 | M,10/16 | Chapter 2: Context-Free Languages
Converting a CFG to a PDA The pumping lemma for CFL |
|||
| W, 10/18 | Solve homework 6
Chapter 2: Context-Free Languages The pumping lemma for CFL |
hw7: Ch. 2 | hw6 | ||
| F, 10/20 | Midterm exam 1
Part 1 of the textbook |
Good luck! | |||
| 8 | M, 10/23 | Chapter 2: Context-Free Languages
The pumping lemma for CFL proving that anbncn is not CF proving that aibjck 0≤i≤j≤k is not CF proving that ww is not CF proving that the C language is not CF |
|||
| W, 10/25 | Return the first exam
( grades )
Solve homework 7 Chapter 2: Context-Free Languages wrap-up: the big picture ( jpg ) ( postscript ) Chapter 3: The Church-Turing Thesis Turing machines Definition, examples |
hw8: Ch. 3 | hw7 | ||
| F, 10/27 |
Chapter 3: The Church-Turing Thesis
Turing machines formal definition configuration of a TM definition of Turing-recognizable definition of Turing-decidable Turing-recognizability TM for {02n | n ≥ 0} |
||||
| 9 | M, 10/30 |
Chapter 3: The Church-Turing Thesis
Turing machines TM for {02n | n &ge 0} TM for {w#w | w ∈ {0,1}* } TM for multiplication TM for {aibjck | i x j = k and i,j,k ≥ 1} TM for {x1#x2# ... #xl | each xiw ∈ {0,1}* and xi ≠ xj for each i ≠ j } |
|||
| W, 11/01 |
Solve homework 8
Chapter 3: The Church-Turing Thesis Variants of Turing machines Universal Turing machine Stay-put TMs Multitape TMs |
hw9: Ch. 3, 4 | hw8 | ||
| F, 11/03 |
Chapter 3: The Church-Turing Thesis
Variants of Turing machines Nondeterministic TMs Enumerators |
||||
| 10 | M, 11/06 |
Chapter 3: The Church-Turing Thesis
The definition of algorithm The Church-Turing thesis Chapter 4: Decidability ADFA, AREX are decidable |
|||
| W, 11/08 | Chapter 4: Decidability | ||||
| F, 11/10 | Chapter 4: Decidability | hw10: Ch. 4, 5 | hw9 | ||
| 11 | M, 11/13 | ||||
| W, 11/15 | hw11: Ch. 5 | hw10 | |||
| F, 11/17 | Midterm exam 2
Part 2 of the textbook |
Good luck! | |||
| -- | M, 11/20 | Thanksgiving recess | |||
| W, 11/22 | Thanksgiving recess | ||||
| F, 11/24 | Thanksgiving recess | ||||
| 12 | M, 11/27 | ||||
| W, 11/29 | hw12: Ch. 5 | hw11 | |||
| F, 12/01 | |||||
| 13 | M, 12/04 | ||||
| W, 12/06 | hw13: Ch. 7 | hw12 | |||
| F, 12/08 | |||||
| 14 | M, 12/11 | ||||
| W, 12/13 | Problems in P
Problems in NP CLIQUE is in NP NP-completeness ( grades so far ) |
hw13 | |||
| F, 12/22 | |||||
| Finals | W, 12/20 | Final Exam on Wednesday (12/20) at 12:45pm
Place: Rekhi CS Hall G09, same room where the class meets |
Good luck! |
Note: A week-long homework is assigned every Wednesday.
