Theory of Computing

Module overview

This module aims to provide a broad and stimulating introduction to the theory of computing.

Aims and Objectives

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

The relationship between the regular, context-free and recursively enumerable classes of languages, and the state-machines that accept them
The complexity of algorithms and problems, and key complexity classes
The nature and examples of undecidable problems
The diagonalisation proof technique

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

Analyse the complexity of a given algorithm or problem
Ascertain and prove whether or not a given language is regular
Use polynomial-time reduction to reason about the complexity class of a problem
Use the reduction technique to show that a problem is undecidable
Ascertain and prove whether or not a given language is context-free

Learning and Teaching

Teaching and learning methods

The content of this module is delivered through lectures, the module website, directed reading, pre-recorded materials and tutorials. Students work on their understanding through a combination of independent study, preparation for timetabled activities, tutorials, and problem classes, along with formative assessments in the form of problem sheets.

Study time
Type	Hours
Revision	18
Tutorial	12
Preparation for scheduled sessions	6
Wider reading or practice	50
Lecture	36
Completion of assessment task	10
Follow-up work	18
Total study time	150

Resources & Reading list

Textbooks

J. Hein (2002). Discrete Structures, Logic and Computability. Jones and Bartlett.

M. Sipser (1997). Introduction to the Theory of Computation. PWS.

A.J.G. Hey (1996). Feynman Lectures on Computation. Addison Wesley.

D. Harel (1992). Algorithmics: The Spirit of Computing. Addison Wesley.

J. Gruska (1996). Foundations of Computing. Thomson.

J. Barwise and J. Etchemendy (1993). Turing's World. Stanford.

N.D. Jones (1999). Computability and Complexity. MIT Press.

D. Cohen (1996). Introduction to Computer Theory. Wiley.

D.C. Kozen (1999). Automata and Computability. Springer.

A.K. Dewdney (2001). The (new) Turing Omnibus. Henry Holt.

Assessment

Assessment strategy

This module is assessed by a combination of problem sheets and a final assessment in the form of a written examination.

Summative

This is how we’ll formally assess what you have learned in this module.

Breakdown
Method	Percentage contribution
Examination	90%
Problem Sheets	10%