Introduction to Theoretical Computer Science - Lectures

The following is the provisional plan for the course. As we're running the course with a new lecturer, the schedule may differ a bit from previous years.

Week 1
Tue 20 Sep, Lecture 1
Finite Automata. (Revision of Inf1!)
Slides (and condensed version).
Thu 22 Sep, Lecture 2
Regular languages and expressions (partly revision).
Slides (and condensed version).
Week 2
Mon 26 Sep
Coursework 1 issued
Tue 27 Sep, Lecture 3
Non-regular languages, context-free languages and grammars
Slides (and condensed version).
Thu 29 Sep, Lecture 4
Push-down automata, pumping for CFLs
Slides (and condensed version).
Week 3
Tutorial sheet for week 3 tutorials.
Tue 4 Oct, Lecture 5
Chomsky Hierarchy. Register machines. Programming RMs. Examples. Pairing.
Slides (and condensed version).
Thu 6 Oct, Lecture 6
Universal RMs. The Halting Problem (with proof). Other models.
Slides (and condensed version).
Week 4
Tue 11 Oct, Lecture 7
Computable functions. Decision problems and oracles. Reductions. Undecidability proofs. Uniform Halting.
Thu 13 Oct, Lecture 8
Looping. Semi-decidability. Enumeration. Looping revisited. Uniform Halting revisited.
Week 5
Tue 18 Oct, Lecture 9
UH continued. Beyond UH. Primitive recursion and partial recursion. Arithmetical hierarchy. (Not official part of course).
Thu 20 Oct, Lecture 10
No lecture; Q&A session if requested
Fri 21 Oct
Coursework 1 due at 12:00
Week 6
Mon 24 Oct
Coursework 2 issued
Tue 25 Oct, Lecture 11
Complexity of algorithms and problems. Polynomial time. Polynomial reductions. Outside P.
Thu 27 Oct, Lecture 12
Non-determinism. The class NP. NP-completeness and statement of Cook-Levin.
Week 7
Tue 1 Nov, Lecture 13
Proof of Cook-Levin.
Thu 3 Nov, Lecture 14
More NP problems. Beyond NP.
Week 8
Tue 8 Nov, Lecture 15
Syntax and semantics of untyped lambda-calculus.
Thu 10 Nov, Lecture 16
Recursion and the Y combinator. Simple types.
Week 9
Tue 15 Nov, Lecture 17
Proof systems for simple types. Properties of simple typing. Recursion in a typed language. Extensions, let, letrec.
Thu 17 Nov, Lecture 17
possible optional lecture
Fri 18 Nov
Coursework 2 due at 12:00
Week 10
Possible fun lectures

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