C. Moore. Smooth maps of the interval and the real line capable of universal computation. Technical report, Santa Fe Institute, 1993. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Hierarchy of Discrete-Time Dynamical Systems - Geurts (1994) (2 citations) (Correct)
....different dynamical systems. If a dynamical is able to simulate another dynamical system, the former is more powerful than the latter. Of course, it can happen that the latter is also able to simulate the former. Then, both systems are equivalent. Several results exist on simulation (among others, [16, 12, 22, 23, 24, 13, 25, 26]) We consider here the most simple definition of simulation we have found in the literature. Definition 7.1 Simulation Let (X; f) and (Y; g) be two dynamical systems. Then f simulates g iff there exists an encoding function OE : Y X and a decoding function : X Y , such that 9m 0 : 8y 2 ....
.... CRF = 0; 1] F; 0; 1] 0; 1] fi) an encoding function OE and a decoding function such that the continuous real function simulates the cellular automaton in one step (i.e. m = 1) CA(u) CRF m (OE(u) Hierarchy of Dynamical Systems 17 The results of this section mainly come from [26]. Another approach is discribed in [15] Here we work with cellular automata spaces and reals from the interval [0; 1] or more precisely, from a subset of [0; 1] which is a Cantor set. Every configuration of the cellular space G Z can be transformed into a state of G N : c Gamma2 c ....
C. Moore. Smooth maps of the interval and the real line capable of universal computation. Technical report, Santa Fe Institute, 1993.
Hierarchy of Discrete-Time Dynamical Systems, a Survey - Geurts (1995) (Correct)
....steps is independent from the input considered. If A simulates B, then A is more powerful than B but this is only a weak result. If one is able to show the converse, both systems are said to be equivalent. In this case, we have a stronger result. Several results exist on simulation (among others, [22, 23, 25, 26, 28, 27, 32, 33]) We consider here the most simple definition of simulation we have found in the literature. Definition 7.1 Simulation Let (X; f) and (Y; g) be two dynamical systems. Then f simulates g iff there exists an encoding function OE : Y X and a decoding function : X Y , such that 9m 0 : 8y 2 ....
.... to find a continuous real function CRF = 0; 1] F; 0; 1] 0; 1] fi) an encoding function OE and a decoding function such that the continuous real function simulates the cellular automaton in one step (i.e. m = 1) CA(u) CRF m (OE(u) The results of this section mainly come from [33]. Another approach is described in [4] Here we work with cellular automata spaces and reals from the interval [0; 1] or more precisely, from a subset of [0; 1] which is a Cantor set. Every configuration of the cellular space G Z can be transformed into a state of G N : c Gamma2 c ....
C. Moore. Smooth maps of the interval and the real line capable of universal computation. Tech. Rep. 93-01-001, Santa Fe Institute, 1993.
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