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CDMTCS Research Report Series Pre-Proceedings of the Workshop CDMTCS Research Report Series Pre-proceedings of the Workshop “Physics and Computation” 2008 C. S. Calude1, J. F. Costa2 (eds.) 1University of Auckland, NZ, 2University of Wales Swansea, UK CDMTCS-327 July 2008 Centre for Discrete Mathematics and Theoretical Computer Science Cristian S. Calude and Jos´eF´elixCosta (eds.) PHYSICS AND COMPUTATION (Renaissance) International Worshop Vienna, Austria, August 25{28, 2008 Pre-proceedings Preface In the 1940s, two different views of the brain and the computer were equally important. One was the analog technology and theory that had emerged before the war. The other was the digital technology and theory that was to become the main paradigm of computation.1 The outcome of the contest between these two competing views derived from technological and epistemological arguments. While digital technology was improving dramatically, the technology of analog machines had already reached a significant level of development. In particular, digital technology offered a more effective way to control the precision of cal- culations. But the epistemological discussion was, at the time, equally relevant. For the supporters of the analog computer, the digital model | which can only process informa- tion transformed and coded in binary | wouldn't be suitable to represent certain kinds of continuous variation that help determine brain functions. With analog machines, on the contrary, there would be few or no layers between natural objects and the work and structure of computation (cf. [4, 1]). The 1942{52 Macy Conferences in cybernetics helped to validate digital theory and logic as legitimate ways to think about the brain and the machine [4]. In particular, those conferences helped made McCulloch-Pitts' digital model of the brain [3] a very influential paradigm. The descriptive strength of McCulloch-Pitts model led von Neumann, among others, to seek identities between the brain and specific kinds of electrical circuitry [1]. This was perhaps the first big event that brought together physicists and the (fathers of) computation theory. Physics and computation theory have interacted from the early days of computing. After a joint start we witnessed the famous late 1950s divorce (fuelled by the hope of doing machine-independent computation) only to realise in the 1980s that, ultimately, physics laws permit computation. As a consequence the first important group of questions have gravitated around the constraints (known) physical laws put on (realisable) computers and computations. As a typical example we cite Lloyd's paper [2]. Quantum computing, relativistic computing, and, more recently, wireless sensor net- works (sensornets) are three examples of different types of computations which differ from classical computation because of physical constraints. While the first two paradigms don't deserve any special introduction the third one does. Sensornets is a computing platform that blends computation, sensing and communication with a physics environment (see [5]). While classical complexity theory deals with time and space resources and their generalisa- tions, sensornets have pointed to a new computational resource: energy. These ideas lead to the urgent need of a theory of computational energy complexity, a subject some people are already thinking about. 1For example, students at MIT could at that time learn about differential analysers and electronic circuits for binary arithmetic [4]. 3 Secondly, but not less important, is the flow of ideas coming from computability the- ory to physics. Looking at physics with a guided computation/information eye we can ask: What, if anything, do the theories of computation and information can say about physics, what physical laws can be deduced using Wheeler's dictum \it from bit"? Com- putational physics has emerged, along with experiment and theory, as the third, new and complementary, approach to discovery in physics. There is a long tradition of workshops on \Physics and Computation" inaugurated by the famous 1982 meeting whose proceedings have been published in a special issue of the Int. J. Theor. Phys. Volume 21, Numbers 3{4, April (1982) which starts with Toffoli’s programatic article \Physics and computation" (pp. 165{175). In a first organisational act of re-inaugurating the series of workshops on \Physics and Computation", we decided to invite twenty eight reputable researchers from the border- lines between computation theory and physics, but also from those sciences that interact strongly with physics, such like chemistry (reaction-diffusion model of computation), biol- ogy (physical-chemical driven organisms), and economic theory (macro-economic models), covering as much as possible all active fields on the subject. Nineteen researchers answer yes to our call and the pre-proceedings of this workshop is the product of their work. Our second act will be to organise next year a second workshop with invited lectures and con- tributed talks, now moving towards a more standard workshop or even a small conference. The main fields covered by this event are (a) analog computation, (b) experimental computation, (c) Church-Turing thesis, (d) general dynamical systems computation, (e) general relativistic computation, (f) optical computation, (g) physarum computation, (h) quantum computation, (i) reaction-diffusion computation, (j) undecidability results for physics and economic theory. r The organisers of this event are grateful for the highly appreciated work done by the reviewers of the papers submitted to the workshop. These experts were: Samson Abramsky, Andrew Adamatzki, Edwin Beggs, Udi Boker, Olivier Bournez, Caslavˇ Brukner, Manuel Lameiras Campagnolo, S. Barry Cooper, Ben De Lacy Costello, Jean-Charles Del- venne, Francisco D´oria,Fernando Ferreira, J´er^omeDurand-Lose, Lu´ısM. Gomes, Jerzy G´orecki, Daniel Gra¸ca,Emmanuel Hainry, Andrew Hodges, Mark Hogarth, Bruno Loff, Aono Masashi, Cris Moore, Jerzy Mycka, Istv´anN´emeti,James M. Nyce, Kerry Ojakian, Oron Shagrir, Andrea Sorbi, Mike Stannett, Karl Svozil, Cristof Teuscher, John V. Tucker, Kumaraswamy Velupillai, Philip Welch, Damien Woods, Martin Ziegler, Jeffery Zucker. We extend our thanks to all members of the local Conference Committee of the Confer- ence UC'2008, particularly to Aneta Binder, Rudolf Freund (Chair of UC'2008), Franziska Gusel, and Marion Oswald of the Vienna University of Technology for their invaluable organisational work. 4 The venue for the conference was the Parkhotel Sch¨onbrunn in immediate vicinity of Sch¨onbrunn Palace, which, together with its ancillary buildings and extensive park, is by virtue of its long and colourful history one of the most important cultural monuments in Austria. Vienna, located in the heart of central Europe, is an old city whose historical role as the capital of a great empire and the residence of the Habsburgs is reflected in its architectural monuments, its famous art collections and its rich cultural life, in which music has always played an important part. The workshop was partially supported by the Institute of Computer Languages of the Vienna University of Technology, the Centre for Discrete Mathematics and Theoretical Computer Science of the University of Auckland, the Kurt G¨odelSociety, and the OCG (Austrian Computer Society); we extend to all our gratitude. C. S. Calude, J. F. Costa Auckland, NZ, Swansea, UK References [1] S. J. Heims. John von Neumann and Norbert Wiener: From Mathematics to the Tech- nologies of Life and Death, MIT Press, 1980. [2] S. Lloyd. Ultimate physical limits of computation, Nature, 406:1047{1054, 2000. [3] W. S. McCulloch and W. Pitts. A logical calculus of the ideas immanent in nervous activity, Bulletin of Mathematical Biophysics, 5:115{133, 1943. [4] J. M. Nyce. Nature's machine: mimesis, the analog computer and the rhetoric of tech- nology. In R. Paton (ed), Computing with Biological Metaphors, 414-423, Chapman & Hall, 1994. [5] F. Zhao. The technical perspective, Comm. ACM, 51, 7 : 98, July (2008). 5 Contents 1 Introduction . 3 2 Andrew Adamatzki. From reaction-diffusion to Physarum computing . 9 3 Edwin Beggs, John V. Tucker. Computations via Newtonian and relativistic kinematic systems . 31 4 Udi Boker, Nachum Dershowitz. The influence of the domain interpretation on computational models . 49 5 Olivier Bournez, Philippe Chassaing, Johanne Cohen, Lucas Gerin, Xavier Koegler. On the convergence of a population protocol when population goes to infinity . 69 6 Caslavˇ Brukner. Quantum experiments can test mathematical undecidabil- ity (Paper included in the Proceedings of UC 2008, Lecture Notes in Com- puter Science 5204.) ............................... 83 7 S. Barry Cooper. Emergence as a computability{theoretic phenomenon . 83 8 Newton C. A. da Costa, Francisco Ant´onioD´oria. How to build a hyper- computer . 106 9 Jean-Charles Delvenne. What is a universal computing machine? . 121 10 J´er^omeDurand-Lose. Black hole computation: implementation with signal machines . 136 11 Jerzy G´orecki, J. N. Gorecka, Y. Igarashi. Information processing with structured excitable medium . 159 12 Daniel Gra¸ca,Jorge Buescu, Manuel Lameiras Campagnolo. Computational bounds on polynomial differential equations . 183 13 Mark Hogarth. A new problem for rule following . 204 14 Istv´anN´emeti,Hajnal Andr´eka, P´eterN´emeti. General relativistic hyper- computing and foundation of mathematics . 210 15 Mike Stannett. The Computational Status of Physics: A Computable For- mulation of Quantum Theory . 230 16 Karl Svozil, Josef Tkadlec. On the solution of trivalent
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