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Theory 3: Computability & Complexity - COM00023I

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  • Department: Computer Science
  • Credit value: 10 credits
  • Credit level: I
  • Academic year of delivery: 2022-23

Module summary

Computability and Complexity

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Module will run

Occurrence Teaching period
A Autumn Term 2022-23

Module aims

The aim of this module is to introduce basic concepts and results in computability theory and complexity theory. In particular, students will learn the concepts of Turing-recognizable languages and Turing-computable functions, and the difference between solvable and unsolvable problems. They will be able to prove unsolvability by reduction. They will understand the time and space complexity of Turing machines, and complexity classes such as P, NP, PSpace, NPSpace and NPC. They will be able to prove NP-completeness by reduction.

Module learning outcomes

T301

Determine a language’s place in the Chomsky hierarchy (regular, context-free, context-sensitive or recursively enumerable).

T302

Provide examples of unsolvable problems.

T303

Prove that a problem is unsolvable by reducing a known unsolvable problem to it.

T304

Explain the Church-Turing thesis and its significance.

T305

Define the classes P and NP, and explain their relation to the class ExpTime.

T306

Explain the significance of NP-completeness and provide examples of NP-complete problems.

Indicative assessment

Task % of module mark
Online Exam -less than 24hrs (Centrally scheduled) 100

Special assessment rules

None

Indicative reassessment

Task % of module mark
Online Exam -less than 24hrs (Centrally scheduled) 100

Module feedback

Feedback is provided through work in practical sessions, revision classes, and after the final assessment as per normal University guidelines.

Indicative reading

**** Martin, John C., Introduction to Languages and the Theory of Computation (4th ed.), McGraw Hill, 2010

** Rich, Elaine, Automata, Computability and Complexity, Pearson Education, 2008

** Sipser, Michael, Introduction to the Theory of Computation (3rd ed.), South-Western College Publishing, 2012

* Hopcroft, John E. and Motwani, Rajeev and Ullman, Jeffrey D., Introduction to Automata Theory, Languages and Computation (3rd ed.), Pearson Education, 2013

* Arora, Sanjeev and Barak, Boaz, Computational Complexity: A Modern Approach, Cambridge University Press, 2009

++ Garey, Michael R. and Johnson, David S., Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman, 1979


The information on this page is indicative of the module that is currently on offer. The University constantly explores ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary. In some instances it may be appropriate for the University to notify and consult with affected students about module changes in accordance with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.