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Page 7079 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
Montclair, NJ) On the construction of state diagrams for cellular automata with additive rules.  ...  Results are given which specify the state diagrams for CAs over GF(2) having from three to forty cells with a sum-of-nearest-neighbors local transition rule for both periodic and null boundary conditions  ... 

A Particular Universal Cellular Automaton

Nicolas Ollinger, Gaétan Richard
2009 Electronic Proceedings in Theoretical Computer Science  
We obtain a high-level construction for a new smallest intrinsically universal cellular automaton with 4 states.  ...  In the present paper, we investigate the use of particles and collisions for constructions involving an infinite number of interacting particles.  ...  For a detailled survey of universality of cellular automata, see [8] . For dimension two or above, the intrinsically universal cellular automaton constructed by E. R.  ... 
doi:10.4204/eptcs.1.20 fatcat:srs4zvqzj5fq5fznmabocuogyy

Four states are enough!

N. Ollinger, G. Richard
2011 Theoretical Computer Science  
This paper presents a 1D intrinsically universal cellular automaton with four states for the first neighbor's neighborhood, improving on the previous lower bound and getting nearer to the Turing universality  ...  Construction and proof rely on a combination of bulking techniques with programming using particles and collisions.  ...  In Section 3, the construction of small universal cellular automata is discussed. In Section 4, the details of the construction of a 4-states intrinsically universal cellular automaton are given.  ... 
doi:10.1016/j.tcs.2010.08.018 fatcat:5upj3ixcvnfvnmzqcfxawt76ku

Visualizing computation in large-scale cellular automata [article]

Hugo Cisneros, Josef Sivic, Tomas Mikolov
2021 arXiv   pre-print
We propose methods for coarse-graining cellular automata based on frequency analysis of cell states, clustering and autoencoders.  ...  Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution.  ...  Experiments begin by sampling 3600 cellular automata rules with 3 or 4 states. We apply the complexity metric on a randomly initialized simulation on a 512 × 512 grid of cells.  ... 
arXiv:2104.01008v1 fatcat:kcum4kkshfh6je6lnpkh4uvzvi

Programmable Cellular Automata Based Efficient Parallel AES Encryption Algorithm

Debasis Das, Rajiv Misra
2011 International journal of network security and its applications  
CA consists of two components 1) a set of cells and 2) a set of rules . Programmable Cellular Automata(PCA) employs some control signals on a Cellular Automata(CA) structure.  ...  This paper deals with the cryptography for a parallel AES encryption algorithm based on programmable cellular automata. This proposed algorithm based on symmetric key systems.  ...  Procedure to Construct Transition Diagram Considering the rule vector < 51,51,195,153> with length 4 so, the total number of states are 2 4 = 16 states means 0000 to 1111.  ... 
doi:10.5121/ijnsa.2011.3615 fatcat:jjgcruvpqbafzfml4jiuhvdleq

Cellular Learning Automata and Its Applications [chapter]

Amir Hosein Fathy Navid, Amir Bagheri
2013 Emerging Applications of Cellular Automata  
It is shown that the synchronous Cellular Learning Automata converges to a globally stable state for a class of rules called commutative rules.  ...  Constructing Voronoi Diagrams Naive Approach A naive approach to construct a Voronoi diagram is to determine the region for each site one at a time.  ... 
doi:10.5772/52953 fatcat:4l32ozg3rvcufcrqqqmnoqyg6u

Complex dynamics in life-like rules described with de Bruijn diagrams: Complex and chaotic cellular automata

Paulina A. Leon, Genaro J. Martinez, Sergio V. Chapa-Vergara
2012 2012 International Conference on High Performance Computing & Simulation (HPCS)  
De Bruijn diagrams have been used as a useful tool for the systematic analysis of one-dimensional cellular automata (CA).  ...  Such analysis is concentrated mainly in two evolution rules: the famous Game of Life (complex CA) and the Diffusion Rule (chaotic CA ).  ...  León (scholarship: 50730 ) would like to thank CINVESTAV and CONACYT for their great support.  ... 
doi:10.1109/hpcsim.2012.6266919 dblp:conf/ieeehpcs/LeonMV12 fatcat:cayttukkcraltowslzxqooylye

Permutive One-Way Cellular Automata and the Finiteness Problem for Automaton Groups [chapter]

Martin Delacourt, Nicolas Ollinger
2017 Lecture Notes in Computer Science  
We provide a rst undecidability result on the dynamics of one-way permutive cellular automata, arguing in favor of the undecidability of the niteness problem for reset Mealy automata.  ...  The decidability of the niteness problem for automaton groups is a well-studied open question on Mealy automata.  ...  Cellular automata A one-way cellular automaton (OCA) F is a triple (X, r, δ) where X is the nite set of states, r is the radius and δ : X r+1 → X is the local rule of the OCA.  ... 
doi:10.1007/978-3-319-58741-7_23 fatcat:nu7u7bhvh5f5hbwnt26j5ar5pe

Computation in Cellular Automata: A Selected Review [chapter]

Melanie Mitchell
2005 Non-Standard Computation  
Acknowledgments Thanks to Jim Crutchfield, Howard Gutowitz, Jim Hanson, Chris Langton, Cris Moore, and Mats Nordahl for many discussions about cellular automata and for comments on an earlier draft of  ...  Research Agency and the Office of Naval Research (N00014-95-1-0975).  ...  Figure 15 gives two space-time diagrams displaying the behavior of this rule on two initial conditions, one with ρ 0 < 1/2 and the other with ρ 0 > 1/2.  ... 
doi:10.1002/3527602968.ch4 fatcat:6elcgxgiy5bjrencagl6uay2hq

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

2003 Mathematical Reviews  
The 6-state solution of the firing synchronization problem is also shown using signal diagrams. The trellis CA and computations on grids are also studied through signal diagrams.  ...  Some of the known results for one-dimensional CA rules 1-256 are summarized in several tables at the end of this chapter of the book.  ... 

Number conservation via particle flow in one-dimensional cellular automata [article]

Markus Redeker
2022 arXiv   pre-print
This paper contains two related constructions by which one can find all one-dimensional number-conserving cellular automata with one kind of particle.  ...  A number-conserving cellular automaton is a simplified model for a system of interacting particles.  ...  Acknowledgement I would like to thank Barbara Wolnik for helpful comments on an earlier version of this text.  ... 
arXiv:1907.06063v3 fatcat:2qrqcef7ivevnmkymvqrn4oruy

Investigation of Rule 73 as Case Study of Class 4 Long-Distance Cellular Automata [article]

Lucas Kang
2013 arXiv   pre-print
Namely, "long-distance cellular automata" (LDCA), a construct that had been described in the past, but never studied.  ...  Cellular automata (CA) have been utilized for decades as discrete models of many physical, mathematical, chemical, biological, and computing systems.  ...  This gives us an upper bound on the length of time between consecutive emerging pieces of moving data, which means that it is indeed possible to space the ossifiers in a fixed way so that they will always  ... 
arXiv:1310.3311v1 fatcat:4t24y6mw4bekfdnqb5bby4e754

Computational Design Thinking through Cellular Automata: Reflections from Design Studios

Pınar Çalışır Adem, Gülen Çağdaş
2020 Journal of Design Studio  
For these reasons, Cellular Automata have an important role in the development of computational design thinking in design studios with different concepts and setups.  ...  After finding matching concepts and comparisons of Cellular Automata methods used in two design studios, the concept of 'computation' in Cellular Automaton studies and contributions of using this generative  ...  In this model, the process started with definitions of the initial configuration of cubes, states and rules for generation and testing.  ... 
doi:10.46474/jds.816833 fatcat:awrkuemckbgx7j6xtfp6ryahhi

Random Expansion Method for the Generation of Complex Cellular Automata [article]

Juan Carlos Seck-Tuoh-Mora, Norberto Hernandez-Romero, Joselito Medina-Marin, Genaro J. Martinez, Irving Barragan-Vite
2020 arXiv   pre-print
Frequently, this type of automata has been found through either an exhaustive search or a meticulous construction of the evolution rule.  ...  Furthermore, the random way of defining complex cellular automata was studied by using mean-field approximations for various states and local entropy measures.  ...  Acknowledgment This study was supported by the National Council for Science and Technology (CONACYT) with the project numbers CB-2014-237323 and CB-2017-2018-A1-S-43008, along with IPN Collaboration Network  ... 
arXiv:2009.09515v1 fatcat:qteeju7ya5cvteqcsreirdmyem

Construction of an Improved English Teaching Model Based on Cellular Automata

Chunyan Wang, Tongguang Ni
2022 Scientific Programming  
In addition, this paper constructs the functional structure of the system and conducts system verification through experimental research.  ...  In order to improve the effect of college English teaching reform, this paper puts cellular automata English into English teaching simulation and uses the cellular automata model to study the behavior  ...  cellular automata-evolving languages of these rules.  ... 
doi:10.1155/2022/9307770 fatcat:yiz7gy3lyrcuvd7wspxa5a3jeu
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