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FUIN
2006

Decidability and Universality in Symbolic Dynamical Systems

13 years 11 months ago
Decidability and Universality in Symbolic Dynamical Systems
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.
Jean-Charles Delvenne, Petr Kurka, Vincent D. Blon
Added 12 Dec 2010
Updated 12 Dec 2010
Type Journal
Year 2006
Where FUIN
Authors Jean-Charles Delvenne, Petr Kurka, Vincent D. Blondel
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