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On the Complexity of Limit Sets of Cellular Automata Associated with Probability Measures
[article]
2006
arXiv
pre-print
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It is a refinement of the classical notion of omega-limit sets dealing with the typical long term behavior of cellular automata. ...
We study the notion of limit sets of cellular automata associated with probability measures (mu-limit sets). This notion was introduced by P. Kurka and A. Maass. ...
) = { ω (01) ω , ω (10) ω }. ⊓ ⊔ We will now give a characterization of the persistent language of non sensitive cellular automata. ...
arXiv:cs/0604007v2
fatcat:asbf3p4xnvbwzi5xgztjnvlymm
On the limit set of some universal cellular automata
1993
Theoretical Computer Science
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For this class of cellular automata we prove that the associated limit language is regular. ...
B- (4) Limi[ set of unitlersal cellular automata
In block IB the size of the blocks of states E+ vary from 2 to 7. ...
doi:10.1016/0304-3975(93)90350-3
fatcat:ejgjojpmrff6bjp5kq54ptwjvy
Limit Sets and the Rate of Convergence for One-Dimensional Cellular Automata Traffic Models
[chapter]
2003
Traffic and Granular Flow'01
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A critical exponent of phase transition for one-dimensional cellular automata with conservative law is proposed and it is shown that the exponent represents the asymptotic behavior of the dynamics. ...
After here we denote the shift map by σ. For one-dimensional cellular automata τ : S Z → S Z , the limit set X ∞ = n≥0 τ n X 0 , X 0 = S Z is always well defined. ...
We estimate such phenomena, that is the asymptotic behavior of one-dimensional cellular automata traffic model from initial distribution to the limit distribution with respect to Gibbs measure [1] on the ...
doi:10.1007/978-3-662-10583-2_9
fatcat:s2dw6ftskngozpwyfjuwbwg6im
On the Complexity of Limit Sets of Cellular Automata Associated with Probability Measures
[chapter]
2006
Lecture Notes in Computer Science
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It is a refinement of the classical notion of ω-limit sets dealing with the typical long term behavior of cellular automata. ...
We study the notion of limit sets of cellular automata associated with probability measures (µ-limit sets). This notion was introduced by P. Kůrka and A. Maass in [1]. ...
{ ω (01) ω , ω (10) ω }. ⊓ ⊔ We will now give a characterisation of the persistent language of non sensible cellular automata. ...
doi:10.1007/11821069_17
fatcat:4ky3yqqspbgwxkdhaqw3snqhbm
Revisiting the Rice Theorem of Cellular Automata
[article]
2011
arXiv
pre-print
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This is a refinement of the classical "Rice Theorem" that Kari proved on cellular automata with arbitrary state sets. ...
The limit set of the cellular automaton is the set of configurations which can be reached arbitrarily late in the evolution. ...
For any nontrivial property P over the limit sets of nonsurjective cellular automata on ¾, there exist two cellular automata G 0 , G 1 on alphabet ¾ sharing the same quiescent state q ∈ ¾, and such that ...
arXiv:1001.0253v4
fatcat:gt63drfonzcv3euzkgogglzzsm
Revisiting the Rice Theorem of Cellular Automata
2010
Symposium on Theoretical Aspects of Computer Science
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This is a refinement of the classical "Rice Theorem" that Kari proved on cellular automata with arbitrary state sets. ...
The limit set of the cellular automaton is the set of configurations which can be reached arbitrarily late in the evolution. ...
For any nontrivial property P over the limit sets of nonsurjective cellular automata on ¾, there exist two cellular automata G 0 , G 1 on alphabet ¾ sharing the same quiescent state q ∈ ¾, and such that ...
doi:10.4230/lipics.stacs.2010.2474
dblp:conf/stacs/GuillonR10
fatcat:mwmnqjguzbfk5mlbcenzmkaoqy
Computation theory of cellular automata
1984
Communications in Mathematical Physics
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The limit sets generated by some classes of cellular automata correspond to regular languages. For other classes of cellular automata they appear to correspond to more complicated languages. ...
The sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages. Many examples are given. ...
Franks, and many of the other participants for their comments. Some of the results given above were obtained using the computer mathematics system SMP [50] . ...
doi:10.1007/bf01217347
fatcat:yrtu66o6xjbkbivnnm3mh2xsqy
Two-dimensional cellular automata
1985
Journal of statistical physics
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A largely phenomenological study of two-dimensional cellular automata is reported. Qualitative classes of behavior similar to those in one-dimensional cellular automata are found. ...
Some global properties of cellular automata can be described by entropies and Lyapunov exponents. Others are undecidahle. ...
Shaw for writing the kernel of our software simulation system for two-dimensional cellular automata in Ridge assembly language. We thank ...
doi:10.1007/bf01010423
fatcat:4tdguoisl5fmraggit5gstkkne
Some applications of information theory to cellular automata
1984
Physica D : Non-linear phenomena
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In this paper general deterministic one-dimensional cellular automata are identified with mappings of the unit interval into itself. ...
A body of related work by Russian authors on probabilistic automata is briefly examined. Important questions about the existence and properties of limiting distributions remain unresolved. ...
The author is grateful to John R. Kinney for useful discussions. ...
doi:10.1016/0167-2789(84)90247-1
fatcat:o3x5ac2djzctddrbo7ufctrw3y
Page 2824 of Mathematical Reviews Vol. , Issue 92e
[page]
1992
Mathematical Reviews
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Summary: “The problem of identification of cellular automata the set of configurations of which is specified on an n-dimensional integer lattice is examined. ...
Summary: “Given a one-dimensional cellular automaton rule f, a block transform of f is a rule 7, f such that there exists between the limit sets of both rules a bijection that replaces each site value ...
Evolution of 2D apoptotic cellular automata
2015
2015 IEEE Congress on Evolutionary Computation (CEC)
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A collection of examples of renderings of evolved cellular automata are provided and steps for additional work to improve the system are outlined. ...
This study generalizes earlier work on evolving 1D apoptotic automata to evolving 2D automata, producing a type of evolved art. ...
the value zero) or until the time limit expired. • If the automata still had living (nonzero) cells at the end of the time limit or if one of the cells at the edge of the cell array was alive, the automata ...
doi:10.1109/cec.2015.7257151
dblp:conf/cec/GarnerA15
fatcat:fljk4ezlzzbqnbe5juj6t2skky
Cellular automata as models of complexity
1984
Nature
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Cellular Automata Cellular automata may serve as suitable models for a wide range of natural systems such as: • The growth of dendritic crystals (snowflakes) • Pigmentation patterns on mollusk shells This ...
,k-1) that update according to a deterministic rule depending on a neighborhood Complex behavior can arise from simple rules Introduction
• Cellular Automata
• Applications
• Types of Cellular Automata ...
Computation theory • For class 3 and 4: • the occurrence of a particular length n site value sequence in infinite time is undecidable. • Decidable in finite time considering initial sequence length n0= ...
doi:10.1038/311419a0
fatcat:kbs6fi7g5vb6dhyuuzf6bdz6xq
On Stable and Unstable Limit Sets of Finite Families of Cellular Automata
[chapter]
2012
Lecture Notes in Computer Science
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In this paper, we define the notion of limit set for a finite family of cellular automata, which is a generalization of the limit set of a single automaton. ...
We prove that the hierarchy formed by increasing the number of automata in the defining set is infinite, and study the boolean closure properties of different classes of limit sets. ...
Acknowledgements We'd like to thank Pierre Guillon for Lemma 12 and for pointing us in the direction of [7] . ...
doi:10.1007/978-3-642-28332-1_43
fatcat:xfdxnzgsszd65ojx5c5n63dylu
Page 4276 of Mathematical Reviews Vol. , Issue 95g
[page]
1995
Mathematical Reviews
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A property is called nontrivial if there are both automata whose limit sets have the property and automata whose limit sets do not have it. ...
The limit set of a cellular automaton consists of all the config- urations that can occur after arbitrarily long computations. ...
Decidability in Group Shifts and Group Cellular Automata
2020
International Symposium on Mathematical Foundations of Computer Science
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Our decidability proofs are based on developing algorithms to manipulate arbitrary group shifts, and viewing the set of space-time diagrams of group cellular automata as multidimensional group shifts. ...
It also turns out that the the trace shift and the limit set can be effectively constructed, that injectivity always implies surjectivity, and that jointly periodic points are dense in the limit set. ...
Then in Section 4 we apply the projections on space-time diagrams of cellular automata to effectively construct their traces and limit sets. ...
doi:10.4230/lipics.mfcs.2020.12
dblp:conf/mfcs/BeaurK20
fatcat:gymyhpgusrfnheallmxxwjc42e
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