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Universality Class of Probabilistic Cellular Automata [chapter]

Danuta Makowiec, Piotr Gnaciński
2002 Lecture Notes in Computer Science  
The Ising-like phase transition is considered in probabilistic cellular automata (CA).  ...  CA with Toom rule and synchronous updating represent the weak universality class of the Ising model, while Toom CA with asynchronous updating fall into the Ising universality class.  ...  This work was supported by Gdańsk University Grant, BW-5400-5-0235-2.  ... 
doi:10.1007/3-540-45830-1_10 fatcat:nschyozweff4fpr4vvz754jtse

Page 2128 of Mathematical Reviews Vol. , Issue 83e [page]

1983 Mathematical Reviews  
From the text: “We study the possibility of constructing a cellular probabilistic automaton, universal over some class of cellular probabilistic automata.  ...  A. 83e:68062 On the question of a universal cellular probabilistic automaton. (Russian) - Cybernetic systems, pp. 35-44, “Metsniereba”’, Tbilisi, 1980.  ... 

Renormalization of Cellular Automata and Self-Similarity

E. Edlund, M. Nilsson Jacobi
2010 Journal of statistical physics  
We study self-similarity in one-dimensional probabilistic cellular automata (PCA) using the renormalization technique.  ...  We discuss how the second result supports a conjecture regarding the universality class for dynamic criticality defined by directed percolation.  ...  Renormalization of probabilistic cellular automata We first formulate the dynamics of cellular automata in terms of matrices.  ... 
doi:10.1007/s10955-010-9974-z fatcat:46tznty7enbz7kyratqia6i2sm

Page 3601 of Mathematical Reviews Vol. , Issue 90F [page]

1990 Mathematical Reviews  
It is natural to consider cellular automata as an idealization of such systems. An extensive study of probabilistic cellular automata (PCAs) in this context has been given by P.  ...  a pedagogical way and then used to analyze the phase diagrams, the critical behavior, and the universality classes of some automata.  ... 

Page 1525 of Mathematical Reviews Vol. 45, Issue 5 [page]

1973 Mathematical Reviews  
We generalize the automaton to the case of n actions and obtain a class of automata with linearly comparing tactics.  ...  Using the notion of cellular matrices the author defines a weakly ergodic probabilistic automaton. Any probabilistic automaton with quasi-definite table is weakly ergodic, but not conversely.  ... 


V. Koubek, J. Kratochvíl
2005 Theoretical Computer Science  
Cellular automata are represented by "A new dimension sensitive property for cellular automata" by Bernardi, Durand, Formenti and Kari, proving that decidability of number decreasing property is sensitive  ...  A unified framework for probabilistic and quantum computation is discussed in "A common algebraic description for probabilistic and quantum computations" by Beaudry, Fernandez and Holzer, and "Universal  ...  some classes of polynomial complexity and non-existence of reducibilities between some classes of exponential complexity.  ... 
doi:10.1016/j.tcs.2005.07.005 fatcat:kgzeybxxybf25brnmx6udotmqm

Page 6962 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
The author investigates the problem of collectives of automata that are universal searchers for the class of all mosaic plane labyrinths. It is known [A. Szepietowski, Inform. Process.  ...  On the minimum universal collectives of automata for plane labyrinths. (English summary) ° Discrete Math. Appl. 3 (1993), no. 6, 555-586.  ... 

Page 808 of Mathematical Reviews Vol. , Issue 82b [page]

1982 Mathematical Reviews  
The description of special probabilistic automata, in the second chapter, is limited to two classes: (1) linear automata, (2) continuous time automata.  ...  the length of the cellular automaton.  ... 

Predictability in Cellular Automata

Alexandru Agapie, Anca Andreica, Camelia Chira, Marius Giuclea, Jesus Gomez-Gardenes
2014 PLoS ONE  
Modelled as finite homogeneous Markov chains, probabilistic cellular automata with local transition probabilities in (0, 1) always posses a stationary distribution.  ...  Previous results on the asynchronous cellular automata have showed that such feature really exists. It is the number of zero-one borders within the automaton's binary configuration.  ...  Probabilistic Cellular Automata In order to describe a probabilistic CA consider the 1-D three neighborhood automaton from the previous section, but with some randomness added to the local transition rule  ... 
doi:10.1371/journal.pone.0108177 pmid:25271778 pmcid:PMC4182702 fatcat:iievljynh5bkvpqe5m5ez5aecy

When are cellular automata random?

J. B. Coe, S. E. Ahnert, T. M. A. Fink
2008 Europhysics letters  
We derive analytical conditions which must be satisfied by random cellular automata and find deterministic and probabilistic cellular automata that satisfy these conditions.  ...  A random cellular automaton is one in which a cell's behaviour is independent of its previous states.  ...  Acknowledgements This work was funded in part by the Defense Advanced Research Projects Agency (DARPA) Fundamental Laws of Biology (FunBio) grant HR 0011-05-1-0057. J.B.C. is supported by FunBio.  ... 
doi:10.1209/0295-5075/84/50005 fatcat:3vgs3izvtncxpk662askz6i3zu


2009 Parallel Processing Letters  
In this thesis, we propose elements of a framework whose goal is to make the manual synthesis of cellular automata rules exhibiting desired global characteristics more programmer-friendly, while maintaining  ...  The ability to obtain complex global behaviour from simple local rules makes cellular automata an interesting platform for massively parallel computation.  ...  For example, it is now believed that most Class 4 cellular automata are universal, while there are no universal automata in other classes.  ... 
doi:10.1142/s0129626409000079 fatcat:i4pmb7td5vekxjv3r3ngavt62q

Cellular automata as a paradigm for ecological modeling

P. Hogeweg
1988 Applied Mathematics and Computation  
Finally we discuss some shortcomings of the cellular-automaton formalism and mention some extensions and generalizations which may remedy these shortcomings. 2. CELLULAR AUTOMATA 2.  ...  We review cellular automata as a modeling formalism and discuss how it can be used for modeling (spatial) ecological processes.  ...  The cellular automata capable of universal computation fall into this class.  ... 
doi:10.1016/0096-3003(88)90100-2 fatcat:pmvygh5pw5gc7ds6pry2revt7y

Cumulative subject index volumes 33–35

1977 Information and Control  
cellular automata, stability, 34, 93 Stochastic integral equations class of mixed type, 34, 339 Stochastic observability and controllability, for nonlinear distributed parameter systems, 34,  ...  radix, 34, 271 Sequential machines probabilistic, two-state completely isolat- ed, 34, 22 Set maximum invariant connection with information trans- mission in one-dimensional cellular space, 33,  ... 
doi:10.1016/s0019-9958(77)90187-5 fatcat:jaxd23nbmva5hdnq37lof736um

Page 6272 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
Fuks, Model- ing diffusion of innovations with probabilistic cellular automata (263-277); A. L. Bardou, P. M. Auger, R. Seigneuric and J.- L.  ...  Delorme, An introduction to cellular automata: some basic definitions and concepts (5-49); Bruno Durand and Zsuzsanna Roka, The game of life: universality revisited (51-74); J.  ... 

Page 6191 of Mathematical Reviews Vol. , Issue 91K [page]

1991 Mathematical Reviews  
The feedback operation and a class of group automata. (Russian) Diskret. Mat. 2 (1990), no. 3, 81-89.  ...  Summary: “Fibonacci representations of integers provide some kinds of universal coding.  ... 
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