Computation at the edge of chaos: phase transitions and emergent computation
CNLS '89 Proceedings of the ninth annual international conference of the Center for Nonlinear Studies on Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks on Emergent computation
On Devaney's definition of chaos
American Mathematical Monthly
On the computational power of dynamical systems and hybrid systems
Theoretical Computer Science - Special issue on universal machines and computations
On topological dynamics of Turing machines
Theoretical Computer Science
Dynamical recognizers: real time language recognition by analog computers
Theoretical Computer Science
On the effect of analog noise in discrete-time analog computations
Neural Computation
Analog computation with dynamical systems
PhysComp96 Proceedings of the fourth workshop on Physics and computation
Neural networks and analog computation: beyond the Turing limit
Neural networks and analog computation: beyond the Turing limit
Computable analysis: an introduction
Computable analysis: an introduction
Modal logic
A new kind of science
Reliable cellular automata with self-organization
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Perturbed Turing Machines and Hybrid Systems
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Decidability and Universality in Symbolic Dynamical Systems
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
Computational complexity of dynamical systems: The case of cellular automata
Information and Computation
Decidability and Universality in Symbolic Dynamical Systems
Fundamenta Informaticae - SPECIAL ISSUE MCU2004
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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.