John V. Tucker

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John Vivian Tucker (born 1952) is a British computer scientist and expert on computability theory, also known as recursion theory. His work has focussed on generalizing the classical theory to deal with all forms of discrete/digital and continuous/analogue data; and on using the generalizations as formal methods for system design.

1 Biography
2 Work on computability and data types
3 References
4 External links

[edit] Biography

Born in Cardiff, Wales, he was educated at Bridgend Boys' Grammar School, where he was taught mathematics, logic and computing. He read mathematics at Warwick University (BA in 1973), and studied mathematical logic and the foundations of computing at Bristol University (MSc in 1974, PhD in 1977). He has held posts at Oslo University, The CWI Amsterdam, and at Bristol and Leeds Universities, before returning to Wales as Professor of Computer Science at Swansea University in 1989.

Tucker founded the British Colloquium for Theoretical Computer Science in 1985 and served as its president from its inception until 1992. He has been Head of Computer Science at Swansea since 1994. He is a Fellow of the British Computer Society and and editor of several international scientific journals and monograph series.

[edit] Work on computability and data types

Classical computability theory is based on the data types of strings or natural numbers. In general, data types, both discrete and continuous, are modelled by universal algebras, which are sets of data equipped with operations and tests. Tucker's theoretical work tackles the problems of: how to define or specify properties of the operations and tests of data types; how to program and reason with them; and how to implement them.

In a series of theorems and examples, starting in 1979, Jan Bergstra and Tucker established the expressive power of different types of equations and other algebraic formulae on any discrete data type. For example, they showed that

On any discrete data type, functions are definable as the unique solutions of small finite systems of equations if, and only if, they are computable by algorithms.

The results combined techniques of universal algebra and recursion theory, including term rewriting and Matiyasevich's theorem.

For the other problems, he and his co-workers have developed two independent disparate generalisations of classical computability/recursion theory, which are equivalent for many continuous data types.

The first generalisation, created with Jeffrey Zucker, focuses on imperative programming with abstract data types and covers specifications and verification using Hoare logic. For example, they showed that:

All computable functions on the real numbers are the unique solutions to a single finite system of algebraic formulae.

The second generalisation, created with Viggo Stoltenberg-Hansen, focuses on implementing data types using approximations contained in the ordered structures of domain theory.

The general theories have been applied as formal methods in microprocessor verifications, data types, and tools for volume graphics and modelling excitable media including the heart.

[edit] References

J A Bergstra and J V Tucker, Equational specifications, complete term rewriting systems, and computable and semicomputable algebras, Journal of the ACM, Volume 42 (1995), pp1194-1230.
V Stoltenberg-Hansen and J V Tucker, Effective algebras, in S Abramsky, D Gabbay and T Maibaum (eds.), Handbook of Logic in Computer Science, Volume IV: Semantic Modelling, Oxford University Press (1995), pp357-526.
V Stoltenberg-Hansen and J V Tucker, Computable rings and fields, in E Griffor (ed.), Handbook of Computability Theory, Elsevier (1999), pp363-447.
J V Tucker and J I Zucker, Computable functions and semicomputable sets on many sorted algebras, in S Abramsky, D Gabbay and T Maibaum (eds.), Handbook of Logic in Computer Science, Volume V: Logic and Algebraic Mehtods, Oxford University Press (2000), pp317-523.
J V Tucker and J I Zucker, Abstract computability and algebraic specification, ACM Transactions on Computational Logic, Volume 5 (2004), pp611-668.