Theory of Computing

Learning Outcomes

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 class PSPACE together with examples of PSPACE-complete 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

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 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
• Analyse the complexity of a given algorithm or problem
• Ascertain and prove whether or not a given language is context-free

Automata theory

• 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

Computability theory

• 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
• PSPACE-Completeness

Resources & Reading list

Textbooks

Hey AJG (1996). Feynman Lectures on Computation. Addison Wesley.

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

Jones ND (1997). Computability and Complexity. MIT.

Dexter C. Kozen (1999). Automata and Computabilty. Springer.

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

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

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

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

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

Dewdney AK (2001). The (new) Turing Omnibus. Henry Holt.

Summative

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

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

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 Information

Repeat type: Internal & External