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On the Complexity of Limit Sets of Cellular Automata Associated with Probability Measures
[article]

2006
*
arXiv
*
pre-print

It is a refinement

arXiv:cs/0604007v2
fatcat:asbf3p4xnvbwzi5xgztjnvlymm
*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*. ...##
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On the limit set of some universal cellular automata

1993
*
Theoretical Computer Science
*

For this class

doi:10.1016/0304-3975(93)90350-3
fatcat:ejgjojpmrff6bjp5kq54ptwjvy
*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. ...##
###
Limit Sets and the Rate of Convergence for One-Dimensional Cellular Automata Traffic Models
[chapter]

2003
*
Traffic and Granular Flow'01
*

A critical exponent

doi:10.1007/978-3-662-10583-2_9
fatcat:s2dw6ftskngozpwyfjuwbwg6im
*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*...##
###
On the Complexity of Limit Sets of Cellular Automata Associated with Probability Measures
[chapter]

2006
*
Lecture Notes in Computer Science
*

It is a refinement

doi:10.1007/11821069_17
fatcat:4ky3yqqspbgwxkdhaqw3snqhbm
*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*. ...##
###
Revisiting the Rice Theorem of Cellular Automata
[article]

2011
*
arXiv
*
pre-print

This is a refinement

arXiv:1001.0253v4
fatcat:gt63drfonzcv3euzkgogglzzsm
*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 ...##
###
Revisiting the Rice Theorem of Cellular Automata

2010
*
Symposium on Theoretical Aspects of Computer Science
*

This is a refinement

doi:10.4230/lipics.stacs.2010.2474
dblp:conf/stacs/GuillonR10
fatcat:mwmnqjguzbfk5mlbcenzmkaoqy
*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 ...##
###
Computation theory of cellular automata

1984
*
Communications in Mathematical Physics
*

*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] . ...

##
###
Two-dimensional cellular automata

1985
*
Journal of statistical physics
*

A largely phenomenological study

doi:10.1007/bf01010423
fatcat:4tdguoisl5fmraggit5gstkkne
*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 ...##
###
Some applications of information theory to cellular automata

1984
*
Physica D : Non-linear phenomena
*

In this paper general deterministic

doi:10.1016/0167-2789(84)90247-1
fatcat:o3x5ac2djzctddrbo7ufctrw3y
*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. ...##
###
Page 2824 of Mathematical Reviews Vol. , Issue 92e
[page]

1992
*
Mathematical Reviews
*

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)
*

A collection

doi:10.1109/cec.2015.7257151
dblp:conf/cec/GarnerA15
fatcat:fljk4ezlzzbqnbe5juj6t2skky
*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*...##
###
Cellular automata as models of complexity

1984
*
Nature
*

*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= ...

##
###
On Stable and Unstable Limit Sets of Finite Families of Cellular Automata
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper, we define

doi:10.1007/978-3-642-28332-1_43
fatcat:xfdxnzgsszd65ojx5c5n63dylu
*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] . ...##
###
Page 4276 of Mathematical Reviews Vol. , Issue 95g
[page]

1995
*
Mathematical Reviews
*

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
*

Our decidability proofs are based

doi:10.4230/lipics.mfcs.2020.12
dblp:conf/mfcs/BeaurK20
fatcat:gymyhpgusrfnheallmxxwjc42e
*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*. ...
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