Theory of Computing

Module overview

Aims and Objectives

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

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

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

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
Completion of assessment task	10
Wider reading or practice	50
Lecture	36
Follow-up work	18
Total study time	150

Resources & Reading list

Textbooks

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

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

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

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

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

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

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

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

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

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

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%