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Introduction to Theoretical Computer Science - Lectures

The following is the provisional plan for the course.

Week 1

Tue 19 Sep, Lecture 1

Finite Automata. (Revision of Inf1!)
Slides (and condensed version).

Thu 21 Sep, Lecture 2

Regular languages and expressions (partly revision).
Slides (and condensed version).

Week 2

Mon 25 Sep

Coursework 1 will be issued

Tue 26 Sep, Lecture 3

Non-regular languages, context-free languages and grammars

Thu 28 Sep, Lecture 4

Push-down automata, pumping for CFLs

Week 3

Tutorial sheet for week 3 tutorials.

Tue 3 Oct, Lecture 5

Chomsky Hierarchy. Register machines. Programming RMs. Examples. Pairing.

Thu 5 Oct, Lecture 6

Universal RMs. The Halting Problem (with proof). Other models.
Reading:
For more information and technical details of Turing Machines, see either Sipser ch.3 (for the TM formalism) and 4 (for the Halting Theorem).

Week 4

Tutorial sheet for week 4 tutorials.

Tue 10 Oct, Lecture 7

Computable functions. Decision problems and oracles. Reductions. Undecidability proofs. Uniform Halting. Rice's Theorem.
Reading: for reductions and undecidable problems, Sipser ch. 5.

Thu 12 Oct, Lecture 8

Looping. Semi-decidability. Enumeration. Looping revisited. Uniform Halting revisited.

Week 5

Tutorial sheet for week 5 tutorials.

Tue 17 Oct, Lecture 9

Arithmetical hierarchy. (Not official part of course).

Thu 19 Oct, Lecture 10

Q&A session; optional lecture on games.

Fri 20 Oct

Coursework 1 due at 12:00

Week 6

Discuss Coursework 1 solutions in Week 6 tutorials.

Mon 23 Oct

Coursework 2 will be issued

Tue 24 Oct, Lecture 11

Complexity of algorithms and problems. Polynomial time. Polynomial reductions. Outside P.

Thu 26 Oct, Lecture 12

Non-determinism. The class NP. NP-completeness and statement of Cook-Levin.

Week 7

Tutorial sheet for week 7 tutorials.

Tue 31 Oct, Lecture 13

Proof of Cook-Levin. NP-Complete problems.

Thu 2 Nov, Lecture 14

Beyond NP. Polynomial Hierarchy.

Week 8

Tutorial sheet for week 8 tutorials.

Tue 7 Nov, Lecture 15

Syntax and semantics of untyped lambda-calculus.

Thu 9 Nov, Lecture 16

Recursion and the Y combinator. Simple types.

Week 9

Tutorial sheet for week 9 tutorials.

Tue 14 Nov, Lecture 17

Unexamined: More types

Thu 16 Nov, Lecture 18

Unexamined: Types as propositions

Fri 17 Nov

Coursework 2 due at 12:00

Week 10

Possible fun lectures