This module aims to provide a broad and stimulating introduction to the theory of computing
Pre-requisites: COMP1215 and COMP1201
Aims and Objectives
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- 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
- Use the reduction technique to show that a problem is undecidable
- 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 complexity class PSPACE together with examples of PSPACE-complete problems
- The nature and examples of undecidable problems
- The diagonalisation proof technique
- The relationship between the regular, context-free and recursively enumerable classes of languages, and the state-machines that accept them
- The complexity classes P and NP together with examples of NP-complete problems
- The time and space complexity of algorithms and problems
- Finite state automata, regular expressions and regular languages
- The pumping lemma for regular languages
- Closure properties of regular languages
- Context-free grammars and pushdown automata
- Closure properties of context-free languages
- The pumping lemma for context-free languages
- Turing machines, recursively enumerable and recursive languages
- Church-Turing thesis
- Limitations of algorithms: universality, the halting problem and undecidability
Computational complexity theory
- Complexity of algorithms and of problems
- Complexity classes P, NP, PSPACE
- Polynomial-time reduction
- NP-Completeness and Cook's theorem
Learning and Teaching
|Completion of assessment task||8|
|Preparation for scheduled sessions||36|
|Wider reading or practice||12|
|Total study time||150|
Resources & Reading list
Harel D (1992). Algorithmics: The Spirit of Computing. Addison Wesley.
Gruska J (1996). Foundations of Computing. Thomson.
Hey AJG (1996). Feynman Lectures on Computation. Addison Wesley.
Cohen D (1996). Introduction to Computer Theory. Wiley.
Dexter C. Kozen (1999). Automata and Computabilty. Springer.
Sipser M, (1997). Introduction to the Theory of Computation. PWS.
Jones ND (1997). Computability and Complexity. MIT.
Hein J (2002). Discrete Structures, Logic, and Computability. Jones and Bartlett.
Barwise J and Etchemendy J (1993). Turing's World. Stanford.
Dewdney AK (2001). The (new) Turing Omnibus. Henry Holt.
This is how we’ll give you feedback as you are learning. It is not a formal test or exam.Examination Blackboard quizzes
This is how we’ll formally assess what you have learned in this module.
This is how we’ll assess you if you don’t meet the criteria to pass this module.
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
Repeat type: Internal & External