Theory of Computing

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

Knowledge and Understanding

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

• The diagonalisation proof technique
• The complexity class PSPACE together with examples of PSPACE-complete problems
• The time and space complexity of algorithms and problems
• The relationship between the regular, context-free and recursively enumerable classes of languages, and the state-machines that accept them
• The nature and examples of undecidable problems
• The complexity classes P and NP together with examples of NP-complete problems

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

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.