Jan 16-20 |
Administrivia and course goals
Introduction and history; strings
[slides1, slides2] |
String induction
[induction notes, more] [solutions] |
Languages and regular expressions [slides] |
Regular expressions
[solutions] |
Jan 23-27 |
DFAs, product construction
[Automata Tutor] [slides] DFA Proofs |
DFA construction
[solutions] |
Non-determinism, NFAs
Jeff's NFA notes
[slides] |
DFA product construction
[solutions] |
Jan�30-Feb�3 |
NFAs continued, equivalence with DFAs and regular expressions
Jeff's NFA notes
[slides] |
DFA/NFA transformation
[solutions] |
Proving non-regularity via fooling sets
[slides]
[DFA Proofs][Fooling sets guide] |
Proving nonregularity
[solutions] |
Feb 6-10 |
Context-free languages and grammars
[slides]
|
Context-free grammars
[solutions] |
Turing machines: history, formal definitions, examples, variations
[slides]
|
Regular or not?
[solutions] |
Feb 13-17 |
Universal Turing Machine, RAM simulation, P
[UTM slides][complexity slides]
|
Turing machine design
[solutions] |
Optional review for Midterm 1 |
Optional review for Midterm 1 |
Midterm 1: Monday, February 20, 7-9pm
Conflict exam: Tuesday, February 21 |
Feb 20-24 |
Recursion: Hanoi, mergesort
[slides][solving recurrences]
|
Hint: Binary search
[solutions] |
Divide and conquer: linear-time selection, Karatsuba multiplication
[recurrence notes] [slides]
|
Divide and conquer
[solutions] |
Feb�27-Mar�3 |
Backtracking: independent set, longest increasing subsequence
[slides] |
Backtracking
[solutions] |
Dynamic programming: splitting strings, longest increasing subsequence
[slides] |
Dynamic programming
[solutions] |
Mar 6-10 |
More DP: Edit Distance, MIS in trees
[slides]
|
More dynamic programming
[solutions] |
CYK Algorithm, Graphs, basic search
[CYK slides, Graph search slides] |
Yet even still more dynamic programming
Drop deadline
[solutions] |
Mar 13-17 |
Directed graphs, depth-first search
[slides]
|
Graph modeling
[solutions] |
Catch up lecture
[Graph notes]
|
Graph modeling
[solutions] |
Mar 20-24 |
Spring break |
Mar 27-31 |
BFS and Shortest Paths
[slides]
|
Shortest paths
[solutions] |
Shortest Paths with Negative Lengths via DP
[slides]
|
More shortest paths
[solutions] |
Apr 3-7 |
Greedy algorithms
[slides]
|
Greedy
[solutions] |
MST Algorithms
[slides]
|
Optional review for Midterm 2 |
Midterm 2: Monday, April 10, 7-9pm
Conflict exam: Tuesday, April 11 |
Apr 10-14 |
No lecture in lieu of midterm |
MST
[solutions] |
Undecidability: halting problem, diagonalization, reductions
[slides]
|
Undecidability via reductions
[solutions] |
Apr 17-21 |
Polynomial time Reductions
[slides]
|
Self Reductions
[solutions] |
NP, NP-Completeness,
3SAT to Independent Set
[slides][helpful video on P vs NP] |
NP-hardness proofs
[solutions] |
Apr 24-28 |
More NP-hardness reductions: 3-coloring, Hamiltonian cycle
[slides]
|
NP-Hardness, the final chapter
[solutions] |
Undecidability: more reductions, Rice's theorem
[slides]
ICES Forms |
Using Rice's Theorem
ICES Forms
[solutions] |
May 1-5 |
Wrap-up and preliminary review for the final exam |
Review for final |
Reading Day |
|
Final exam: Monday, May 8th, 7-10pm
Conflict exam: May 9th, 9am-noon |