Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
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
Computability with low-dimensional dynamical systems
Theoretical Computer Science
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
On the computational power of dynamical systems and hybrid systems
Theoretical Computer Science - Special issue on universal machines and computations
A family of universal recurrent networks
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
Closed-form analytic maps in one and two dimensions can simulate universal Turing machines
Theoretical Computer Science - Special issue on real numbers and computers
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
Model checking
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
A new kind of science
A theory of complexity for continuous time systems
Journal of Complexity
Cellular automata and intermediate degrees
Theoretical Computer 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
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Universality and cellular automata
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
Computational universality in symbolic dynamical systems
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
Electronic Notes in Theoretical Computer Science (ENTCS)
Computability of countable subshifts
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
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Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as undecidability of a model-checking problem. For Turing machines, counter machines and tag systems, our definition coincides with the classical one. It yields, however, a new definition for cellular automata and subshifts. Our definition is robust with respect to initial condition, which is a desirable feature for physical realizability. We derive necessary conditions for undecidability and universality. For instance, a universal system must have a sensitive point and a proper subsystem. We conjecture that universal systems have infinite number of subsystems. We also discuss the thesis according to which computation should occur at the 'edge of chaos' and we exhibit a universal chaotic system.