transfer matrix; cellular automata; thermal noise; majority vote
Abstract :
[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.
Disciplines :
Physics
Author, co-author :
Lemoy, Rémi ; University of Luxembourg > Faculty of Language and Literature, Humanities, Arts and Education (FLSHASE) > Identités, Politiques, Sociétés, Espaces (IPSE)
Transfer matrix analysis of one-dimensional majority cellular automata with thermal noise
Publication date :
2014
Journal title :
Journal of Physics. A, Mathematical and Theoretical
ISSN :
1751-8113
Publisher :
Iop Publishing Ltd, Bristol, Unknown/unspecified
Volume :
47
Issue :
10
Pages :
105001-11
Peer reviewed :
Peer reviewed
Funders :
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]
Commentary :
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.
