Transformation Semigroups as Constructive Dynamical Spaces

@inproceedings{EgriNagy2010TransformationSA,
  title={Transformation Semigroups as Constructive Dynamical Spaces},
  author={Attila Egri-Nagy and Paolo Dini and Chrystopher L. Nehaniv and Maria J. Schilstra},
  booktitle={OPAALS},
  year={2010}
}
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… 
View via Publisher
researchgate.net
12 Citations
Background Citations
5
Methods Citations
3

12 Citations

Citation Type

Citation Type

The Algebraic View of Computation
TLDR
Computational implementations are special relations between what is computed and what computes it, and the algebraic approach sheds light on the interplay between time and computation.
Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions
TLDR
The goals of this work are to identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this and use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation.
Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov-Zhabotinsky reaction
The Algebraic View of Computation : Implementation , Interpretation and Time
TLDR
Computational implementations are special relations between what is computed and what computes it, and the algebraic approach sheds light on the interplay between time and computation.
Finite Computational Structures and Implementations: Semigroups and Morphic Relations
  • A. Egri-Nagy
  • Computer Science, Mathematics
    Int. J. Netw. Comput.
  • 2017
TLDR
An abstract algebraic definition of classical computation is described by generalizing traditional models to semigroups and implementations are morphic relations between semig groups.
Towards Autopoietic Computing
TLDR
The main concepts of autopoiesis are reviewed and how they could be related to fundamental concepts and theories of computation and the emphasis is on the review of other people’s work in this area as part of a longer-term strategy to develop a formal theory of autopOietic computing.
WP 1 : Cell Biology , Autopoiesis and Biological Design Patterns D 1 . 4 : Mathematical Models of Gene Expression Computing
TLDR
It is shown that the p53-mdm2 system exhibits homoclinic behaviour, and is therefore amenable to a horseshoe map-type of analysis through symbolic dynamics, and that even at a fairly coarse discretisation the automaton derived from it harbours a simple non-abelian group in its holonomy decomposition.
A Research Framework for Interaction Computing
TLDR
The paper recounts the main insights and lessons learned in the past six years across multiple projects, gives a current definition of the problem, and outlines a research programme for how to approach it that will guide the research over the coming years.
Finite Computational Structures and Implementations
  • A. Egri-Nagy
  • Computer Science
    2016 Fourth International Symposium on Computing and Networking (CANDAR)
  • 2016
TLDR
An abstract algebraic definition of classical computation is described, generalizing traditional models to semigroups and allowing the investigation of different computing paradigms (e.g. cellular automata, reversible computing) in the same framework.
Lie Group Analysis of a p53-mdm2 ODE Model
TLDR
A symmetry analysis based on Lie groups of a system of ordinary differential equations modelling the p53-mdm2 regulatory pathway helped reduce the system to a single Riccati equation for a specific choice of parameters, whose oscillatory behaviour appears to be relevant to the bio-computing perspective being discussed in a companion paper.
...
...

References

SHOWING 1-10 OF 36 REFERENCES
Algebraic properties of automata associated to Petri nets and applications to computation in biological systems
Applications of Automata Theory and Algebra via the Mathematical Theory of Complexity to Biology
TLDR
This first published edition has been edited and updated by Chrystopher Nehaniv for the 21st century and sets the stage for the application of algebraic automata theory to areas outside mathematics.
Towards Autopoietic Computing
TLDR
The main concepts of autopoiesis are reviewed and how they could be related to fundamental concepts and theories of computation and the emphasis is on the review of other people’s work in this area as part of a longer-term strategy to develop a formal theory of autopOietic computing.
BIONETS WP 2.2 – PARADIGM APPLICATION AND MAPPING D2.2.9 Mathematical Framework for Interaction Computing with Applications to Security and Service Choreography
TLDR
This work takes as a starting hypothesis that the dynamically stable operation of the cell is critically dependent on two additional forms of structure that are more abstract than physical structure and that can be formalised mathematically as follows: time-independent algebraic structure of the automata modelling the cellular pathways and time-dependent Lie group structure ofthe dynamical systems modelling the same cellular pathways.
Functions and Polynomials over Finite Groups from the Computational Perspective
In the thesis we investigate the connections between arbitrary functions and their realizing polynomials over nite algebras. We study functionally complete algebras, i.e. algebras over which every…
A Research Framework for Interaction Computing
TLDR
The paper recounts the main insights and lessons learned in the past six years across multiple projects, gives a current definition of the problem, and outlines a research programme for how to approach it that will guide the research over the coming years.
Automatic analysis of computation in biochemical reactions
The Church-Turing Thesis: Breaking the Myth
TLDR
This paper identifies and analyzes the historical reasons for widespread belief that no model of computation more expressive than Turing machines can exist, and presents one such model, Persistent Turing Machines (PTMs), which capture sequential interaction, which is a limited form of concurrency.
Introduction to automata theory, languages, and computation, 2nd edition
TLDR
The introduction to formal languages and automata wasolutionary rather than rcvolrrtionary and addressed Initially, I felt that giving solutions to exercises was undesirable hecause it lirrritcd the Chapter 1 fntroduction to the Theory of Computation.
Introduction to Cybernetics.
Abstract : This book contains the collected and unified material necessary for the presentation of such branches of modern cybernetics as the theory of electronic digital computers, theory of…
...
...