Computability and experimental procedures applied to physical systems

Professor John Tucker, Swansea University

In this lecture I will survey some old and new results that try to answer these questions:

1. What are the functions computable by experimental procedures applied to different physical systems?

2. How do they compare with the functions computable by algorithms?

3. Do there exist physical systems that exhibit behaviour is not algorithmically computable?

4. What are the physical limits to computation?

First, I will give some brief background on computability with continuous data, such as real numbers, and will report on my recent work with J I Zucker (McMaster). Second, I will give a progress report on my new research programme with Edwin J Beggs (Swansea) investigating notions of experimental computation using physical theories. One aim is to study the embedding of computational models and non-computable behaviours into small simple subtheories of physical theories in order to explore the boundary between the computable and non-computable inside physical theories. See, for example, Proc Royal Society Series A 463 (2007), 1541-1561.

Some theorems show there exists simple kinematic systems that can compute algorithmically non-computable data. These results give technical insight into the questions above, and shows they are painfully subtle. Although we have a methodology that enables us to make dramatic technical progress, we are also aware that we are stockpiling philosophical problems.

Biography: John V Tucker is Professor of Computer Science at Swansea University. His research interests include: computability theory, algebraic theory of data, specification and programming theory, history and theory of technology.

He was educated in mathematics at Warwick University (BA 1973) and in mathematical logic at Bristol University (MSc 1974, PhD 1975). He held a Royal Society European Programme Fellowship at Oslo (1977-79) and was a researcher at the CWI, Amsterdam (1979-81). After eight years at Leeds University, he returned to his native Wales in 1989. He has been Head of Computer Science since 1994.

Tucker founded the British Colloquium for Theoretical Computer Science in 1985 and served as its President from its inception until 1992. He is a Fellow of the British Computer Society. He is an editor of several international scientific journals and monograph series and managing editor of Journal of Logic and Algebraic Programming (Elsevier).

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