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
Tue 26 Sep, Lecture 3: Postponed due to strike action.
Thu 28 Sep, Lecture 4: Postponed due to strike action.
Week 3
Tutorial sheet for week 3 tutorials.
Mon 2 Oct: Coursework 1 issued
Tue 3 Oct, Lecture 3: Non-regular languages, context-free languages and grammars
Slides (and condensed version).
Thu 5 Oct, Lecture 4: Push-down automata
Slides (and condensed version).
Week 4
Tutorial sheet for week 4 tutorials.
Tue 10 Oct, Lecture 5: Pumping for CFLs, Chomsky Hierarchy. Register machines. Programming RMs. Examples. Pairing.
Slides (and condensed version).
Julian's note on limited registers being enough.
Thu 12 Oct, Lecture 7: Universal RMs. The Halting Problem (with proof). Other models.
Slides (and condensed version).
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 5
Tutorial sheet for week 5 tutorials.
Tue 17 Oct, Lecture 7: Computable functions. Decision problems and oracles. Reductions. Undecidability proofs. Uniform Halting. Rice's Theorem.
Slides (and condensed version).
Reading: for reductions and undecidable problems, Sipser ch. 5.
Thu 19 Oct, Lecture 8: Looping. Semi-decidability. Enumeration. Looping revisited. Uniform Halting revisited.
Slides (and condensed version).
Week 6
Discuss Coursework 1 solutions in Week 6 tutorials.
Tue 24 Oct, Lecture 9: Arithmetical hierarchy. (Not official part of course).
Slides (and condensed version).
Bonus material (Lecture 10): Hintikka and Back and Forth Games
Slides (and condensed version).
Thu 26 Oct: No lecture
Fri 27 Oct: Coursework 1 due at 12:00
Week 7
Tutorial sheet for week 7 tutorials.
Mon 30 Oct: Coursework 2 released (late)
Tue 31 Oct, Lecture 11: Complexity of algorithms and problems. Polynomial time. Polynomial reductions. Outside P. Nondeterminism. The class NP.
Slides (and condensed version).
Reading: Sipser sections 7.1 and 7.2.
Thu 2 Nov, Lecture 12: NP-Hardness. NP-completeness, the Cook-Levin theorem. Some NP-complete problems.
Slides (and condensed version).
Julian's note on reduction details.
Reading: Sipser 7.3 and 7.4.
Week 8
Tutorial sheet for week 8 tutorials.
Tue 7 Nov, Lecture 13: Beyond NP. Polynomial Hierarchy.
Sipser 7.5, then look briefly through ch. 8, 9.1, 10.1- -10.3.
Slides (and condensed version).
Thu 9 Nov, Lecture 14: Syntax and semantics of untyped lambda-calculus.
Slides (and condensed version).
Reading: Pierce Ch. 5 up to page 65 half-way down; plus back-references to previous chapters.
Week 9
Tutorial sheet for week 9 tutorials.
Tue 14 Nov, Lecture 15: Recursion and the Y combinator, Simple types.
Unexamined: Type theory and the Curry-Howard correspondence.
Slides (and condensed version).
Reading: Pierce 9.2, 9.3,9.5, 11 (esp. 11.5 and 11.11), 12.
Phil Wadler's tutorial paper on Curry-Howard.
Thu 16 Nov, Lecture 16: Optional lecture on space complexity
Slides (and condensed version).
Fri 17 Nov: Coursework 2 due at 12:00
Week 10
Tue 21 Nov, Lecture 17: Optional lecture on information and Kolmogorov complexity.
Slides (and condensed version).
Thu 23 Nov, Lecture 18: Optional lectures on Denotational Semantics.
Slides (and condensed version).

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