Reference : Transfer matrix analysis of one-dimensional majority cellular automata with thermal noise
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
http://hdl.handle.net/10993/31616
Transfer matrix analysis of one-dimensional majority cellular automata with thermal noise
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Lemoy, Rémi mailto [University of Luxembourg > Faculty of Language and Literature, Humanities, Arts and Education (FLSHASE) > Identités, Politiques, Sociétés, Espaces (IPSE)]
Mozeika, Alexander [Aalto Univ, Dept Informat & Comp Sci, FI-00076 Aalto, Finland.]
Seki, Shinnosuke [Aalto Univ, Dept Informat & Comp Sci, FI-00076 Aalto, Finland.]
2014
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Iop Publishing Ltd
47
10
105001-11
Yes (verified by ORBilu)
International
1751-8113
Bristol
[en] transfer matrix ; cellular automata ; thermal noise ; majority vote
[en] Thermal noise in a cellular automaton (CA) refers to a random perturbation in its function which eventually leads the automaton to an equilibrium state controlled by a temperature parameter. We study the one-dimensional majority-3 CA under this model of noise. Without noise, each cell in the automaton decides its next state by majority voting among itself and its left and right neighbour cells. Transfer matrix analysis shows that the automaton always reaches a state in which every cell is in one of its two states with probability 1/2 and thus cannot remember even one bit of information. Numerical experiments, however, support the possibility of reliable computation for a long but finite time.
Center of Excellence program of the Academy of Finland ; COMP Centre [251748] ; COIN Centre [251170] ; HIIT Pump Priming grant [902184/T30606] ; Academy of Finland [13266670/T30606]
http://hdl.handle.net/10993/31616
10.1088/1751-8113/47/10/105001
This work is supported by funding from the Center of Excellence program of the Academy of Finland, with the COMP (251748) Centre for Remi Lemoy and the COIN (251170) Centre for Alexander Mozeika (AM). The work by Shinnosuke Seki is financially supported by HIIT Pump Priming grant no. 902184/T30606 and by the Academy of Finland, Postdoctoral Research grant no. 13266670/T30606. AM is thankful for interesting and helpful discussions with ACC Coolen and R Kuhn.

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