Fall 2009
Topics |
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Reference |
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Introduction and Background:
Cardinality of infinite sets, Languages, ${\Sigma}^*$ is countably infinite Set of all languages over a finite alphabet is uncountably infinite |
Monday, August 17
Sipser Chapter 0.
| Introduction Formal languages Cardinality of set of languages | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Deterministic Turing machines Turing-recognizable languages Turing-decidable languages |
Wednesday, August 19
Sipser Chapter 3.
| Deterministic Turing machines Deterministic Turing machines - Examples | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Reasonable variants of Turing machines Multi-tape Turing-machines |
Friday, August 21
Sipser section 3.2.
| Turing machine variants | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Enumerators Nondeterminism - examples |
Monday, August 24
Sipser section 3.2. | Nondeterminism examples | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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NTMs |
Wednesday, August 26
Sipser section 3.2 | NTMs | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Simulation of NTMs by DTMs Encodings |
Friday, August 28
Sipser section 3.2 | NTMs simulation by DTMs Encodings | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Decidability |
Monday, August 31
Sipser section 4.1. | decidability | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Acceptance problem for TMs undecidable |
Wednesday, September 2
Sipser section 4.2. | undecidability | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Test 1 |
Friday, September 4
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Reducibility |
Wednesday, September 9
Sipser sections 5.3, 5.1. | Reductions | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Reducibility |
Friday, September 11
Sipser sections 5.1 and 5.3. | More Reductions | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Rice's theorem Computation histories |
Monday, September 14
Sipser Problem 5.28, section 5.1. | Rice's theorem Computation histories | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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ALL_{CFG} is undecidable |
Wednesday, September 16
Sipser Theorem 5.13. | ALL_{CFG} | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Post Correspondence Problem |
Friday, September 18
Sipser Theorem 5.15. | PCP PCP - an example | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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NP-Completeness |
Monday, September 21
Sipser Sections 7.1, 7.2, 7.3. | NP-Completeness | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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NP-Completeness |
Wednesday, September 23
Sipser Sections 7.3, 7.4 | | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Test 2 |
Friday, September 25
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NP-Reductions |
Monday, September 28
Sipser Section 7.4, Theorem 7.32, Corollary 7.42 | NP-Reductions | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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SUBSET-SUM is NP-Complete |
Wednesday, September 30
Sipser Theorem 7.56 (with a small modification in the proof) | Problem 7.16 Subset-sum | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Hamiltonian Path is NP-Complete 3-Color is NP-Complete |
Friday, October 2
Sipser Theorem 7.46 | Problem 7.27 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Fall recess |
Monday, October 5
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Cook-Levin theorem |
Wednesday, October 7
Sipser Theorem 7.37 | Cook's theorem
Cook-Levin theorem (continued) |
Friday, October 9
Sipser Theorem 7.37 and Corollary 7.42 |
3-Coloring is NP-Complete | The complexity class BPP
Monday, October 12
Sipser section 10.2 |
The complexity class BPP | Acceptance probability amplification
Wednesday, October 14
Sipser section 10.2, Lemma 10.5 | acceptance probability amplification
Test 3
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Friday, October 16
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Polynomial identity testing |
Monday, October 19
Sipser Lemma 10.14, Lemma 10.15 | randomized algorithm for bipartite perfect matching Polynomial identity testing
inequivalence of read-once branching programs |
Wednesday, October 21
Sipser Theorem 10.13 | read-once BP inequivalence
dynamic programming: sequence alignment |
Friday, October 23
KT section 6.6 | dynamic programming
dynamic programming: Bellman-Ford algorithm |
Monday, October 26
KT section 6.8, 6.10 | shortest-paths and negative cycles
dynamic programming: Floyd-Warshall algorithm | Fibonacci heaps
Wednesday, October 28
Floyd-Warshall algorithm
| Fibonacci heaps
Fibonacci heaps |
Friday, October 30
Fibonacci heaps
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Fibonacci heaps |
Monday, November 2
Fibonacci heaps
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Fibonacci heaps | Maximum-flow
Wednesday, November 4
Fibonacci heaps
| Maximum flow
Test 4
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Friday, November 6
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Maximum-flow
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Monday, November 9
Maximum flow
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Maximum-flow Min-Cut theorem
| Bipartite graph matching
Wednesday, November 11
Maximum flow
| Maximum matching in bipartite graphs
A scaling algorithm for maximum-flow
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Friday, November 13
Maximum flow scaling algorithm
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Hopcroft-Karp algorithm for maximum matching in bipartite graphs
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Monday, November 16
HK algorithm
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Hopcroft-Karp algorithm for maximum matching in bipartite graphs
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Wednesday, November 18
HK algorithm
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Test 5
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Friday, November 20
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Fast Fourier Transform Algorithm
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Monday, November 23
FFT algorithm
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Fast Fourier Transform Algorithm
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Wednesday, November 25
FFT algorithm example
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