Group Overview

The 'Theory Group' pursues research in a wide range of topics in Theoretical Computer Science. Please have a look at the theory pages for recent updates.

What is Theoretical Computer Science?

Theoretical Computer Science (TCS) uses mathematical and logical methods to understand the nature of computation and to solve fundamental problems arising through the everyday practical use of computer systems.

TCS owes much of its success to Alan Turing (1912-1954), whom many consider the father of TCS, and to Kurt Gödel (1906-1978), the founder of modern logic. Turing gave a precise definition of the notion of computation through his Turing machines and showed that there exist computing problems that no computer, however powerful, will ever be able to solve. Gödel showed that logical reasoning can be fully formalised and mechanised, but on the other hand, many properties of data structures and computing systems are inherently undecidable, that is neither provable nor disprovable.

Based on Turing's and Gödel's fundamental insights, which showed both the power and the limitations of computation and logic, TCS developed a wide variety of methods to prove the correctness of computing system and to discover software errors before they lead to catastrophic computer failures.  TCS also assesses the inherent difficulty of computing problems, develops efficient new methods to solve hard computing problems and provides powerful methodologies for the development of correct and reliable software.

The main topics of TCS include the Theory of Algorithms, Data Structures, Computability Theory, Computational Complexity, Models of Computation, for example Parallel, Distributed, Concurrent, Probabilistic, and Quantum Computation, Automata Theory and Formal Languages, Information Theory, Logic in Computer Science.

The Swansea Theory Group is internationally renowned for its research in Logic in Computer Science. Active research areas include: Computability Theory, Computational Complexity, Proof Theory, Type Theory, Game Theory, Concurrency, Artificial Intelligence (Satisfiability Solving, Multi-agent Systems, Argumentation Theory, Machine Learning, AI and Law), and Formal Methods (Cyber Security, Blockchain Technology, verification of Railway Control Systems).

The research on Railway Control Systems has lead to the formation of the Swansea Railway Verification Group which also delivered an Impact Case Study.

Another recently form sub group studies the Educational, and Historical and Philosophical Foundation of Computer Science.

Further Project Information