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

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

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

Knowledge and Understanding

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

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

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

Resources & Reading list

Textbooks

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

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

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

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

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

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

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

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

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

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

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%