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Computational Universality in Symbolic Dynamical Systems

  • Jean-Charles Delvenne
  • Petr Kůrka
  • Vincent D. Blondel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3354)

Abstract

Many different definitions of computational universality for various types of systems have flourished since Turing’s work. In this paper, we propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. For Turing machines and tag systems, our definition coincides with the usual notion of universality. It however yields a new definition for cellular automata and subshifts. Our definition is robust with respect to noise on the initial condition, which is a desirable feature for physical realizability.

We derive necessary conditions for universality. For instance, a universal system must have a sensitive point and a proper subsystem. We conjecture that universal systems have an infinite number of subsystems. We also discuss the thesis that computation should occur at the ‘edge of chaos’ and we exhibit a universal chaotic system.

Keywords

Cellular Automaton Temporal Logic Turing Machine Symbolic System Symbolic Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jean-Charles Delvenne
    • 1
  • Petr Kůrka
    • 2
  • Vincent D. Blondel
    • 1
  1. 1.Department of Mathematical EngineeringCatholic University of LouvainLouvain-la-NeuveBelgium
  2. 2.Faculty of Mathematics and PhysicsCharles University of PraguePraha 1Czech Republic

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