Digital Ecosystems. Third International Conference, OPAALS 2010, Aracuju, Sergipe, Brazil, March 22-23, 2010, Revised Selected Papers

Research Article

Transformation Semigroups as Constructive Dynamical Spaces

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  • @INPROCEEDINGS{10.1007/978-3-642-14859-0_19,
        author={Attila Egri-Nagy and Paolo Dini and Chrystopher Nehaniv and Maria Schilstra},
        title={Transformation Semigroups as Constructive Dynamical Spaces},
        proceedings={Digital Ecosystems. Third International Conference, OPAALS 2010, Aracuju, Sergipe, Brazil, March 22-23, 2010, Revised Selected Papers},
        proceedings_a={OPAALS},
        year={2012},
        month={5},
        keywords={},
        doi={10.1007/978-3-642-14859-0_19}
    }
    
  • Attila Egri-Nagy
    Paolo Dini
    Chrystopher Nehaniv
    Maria Schilstra
    Year: 2012
    Transformation Semigroups as Constructive Dynamical Spaces
    OPAALS
    Springer
    DOI: 10.1007/978-3-642-14859-0_19
Attila Egri-Nagy1,*, Paolo Dini2,*, Chrystopher Nehaniv1,*, Maria Schilstra1,*
  • 1: University of Hertfordshire
  • 2: London School of Economics and Political Science
*Contact email: a.egri-nagy@herts.ac.uk, p.dini@lse.ac.uk, c.l.nehaniv@herts.ac.uk, m.j.1.schilstra@herts.ac.uk

Abstract

The informal notion of constructive dynamical space, inspired by biochemical systems, gives the perspective from which a transformation semigroup can be considered as a programming language. This perspective complements a longer-term mathematical investigation into different understandings of the nature of computation that we see as fundamentally important for the realization of a formal framework for interaction computing based on algebraic concepts and inspired by cell metabolism. The interaction computing perspective generalizes further the individual transformation semigroup or automaton as a constructive dynamical space driven by programming language constructs, to a constructive dynamical ‘meta-space’ of interacting sequential machines that can be combined to realize various types of interaction structures. This view is motivated by the desire to map the selforganizing abilities of biological systems to abstract computational systems by importing the algebraic properties of cellular processes into computer science formalisms. After explaining how semigroups can be seen as constructive dynamical spaces we show how John Rhodes’s formalism can be used to define an Interaction Machine and provide a conceptual discussion of its possible architecture based on Rhodes’s analysis of cell metabolism. We close the paper with preliminary results from the holonomy decomposition of the semigroups associated with two automata derived from the same p53-mdm2 regulatory pathway being investigated in other papers at this same conference, at two different levels of discretization.