# Lecture Topics (tentative)

## 1/21 — Turing machine I: the computational model

* Reading: * § 1.1-1.4

## 1/23 — Turing machine II: more on the computational model

* Reading: * § 1.1-1.4

## 1/28 — Turing machine III: computability, reductions

* Reading: * § 1.5.1

## 1/30 — Gödel's incompleteness theorem

* Reading: * § 1.5.2

## 2/4 — (Deterministic) Time Hierarchy Theorem

* Reading: * § 3.1

## 2/6 — NP and NP completeness I: definition, examples

* Reading: * § 2.1, 2.2

## 2/11 — NP hardness reductions

* Reading: * § 2.3

## 2/13 — More reductions, The Cook-Levin theorem

* Reading: * § 2.4

## 2/18 — The Cook-Levin theorem (continued)

* Reading: * § 2.4

## 2/20 — Ladner's theorem and Diagonalization

* Reading: * § 3.3

## 2/25 — February break

## 2/27 — Oracles and limits of diagonalization I

* Reading: * § 3.4

## 3/3 — Oracles and limits of diagonalization II

* Reading: * § 3.4

## 3/5 — co-NP and limits to good characterization (Guest lecturer: Éva Tardos)

* Reading: * § 2.6.1, 2.7.4

Additional notes by David Stuerer (from Fall'15 edition of this course): notes

## 3/10 — PRELIMS 1 (in class)

## 3/12 — Space complexity: introduction, Hierarchy theorem

* Reading: * § 4.1

Extended Spring-break due to Covid-19. All lectures below will be delivered virtually via Zoom.

## 4/7 — Savitch's theorem

* Reading: * § 4.2.1

## 4/9 — Boolean circuits I: examples, upper bounds

* Reading: * § 6.1

## 4/14 — Boolean circuits II: lower bounds

* Reading: * § 6.1

## 4/16 — Boolean circuits III: alternate proof of Cook Levin theorem

* Reading: * § 6.1.2

## 4/21 — Randomized Computation I: probabistic Turing machines, examples

* Reading: * § 7.1, 7.2

## 4/23 — Randomized Computation II: More examples

* Reading: * § 7.2

## 4/28 — Randomized computation III: Error reduction and circuits

* Reading: * § 7.4.1, 7.5.1

## 4/30 — Interactive proofs I: IP and graph non-isomorphism

* Reading: * § 8.1

## 5/5 — Interactive proofs II: IP and graph non-isomorphism

* Reading: * § 8.1, 8.2

## 5/7 — Interactive proofs III: public vs private coins

* Reading: * § 8.3

## 5/12 — Cryptography I: one-time pad, perfect secrecy

* Reading: * § 9.1