Transformation semigroups as constructive dynamical spaces

Attila Egri-Nagy, Paolo Dini, Chrystopher L. Nehaniv, Maria J. Schilstra

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    4 Citations (Scopus)


    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 self-organizing 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.

    Original languageEnglish
    Title of host publicationDigital Ecosystems - Third International Conference, OPAALS 2010, Revised Selected Papers
    Number of pages21
    Publication statusPublished - 1 Dec 2010
    Event3rd International Conference on Digital Ecosystems, OPAALS 2010 - Aracuju, Sergipe, Brazil
    Duration: 22 Mar 201023 Mar 2010

    Publication series

    NameLecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering
    Volume67 LNICST
    ISSN (Print)1867-8211


    Conference3rd International Conference on Digital Ecosystems, OPAALS 2010
    CityAracuju, Sergipe


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