Computational Analysis of One-Dimensional Cellular Automata

“…The de Bruijn diagrams already had been applied in CA (mainly in one dimension case), previously by McIntosh [9], Wolfram [18], Jen [6], Voorhees [15], Sutner [14], among other researchers.…”

Section: Introductionmentioning

confidence: 99%

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

León

Mart́ınez

Chapa-Vergara

2012

2012 International Conference on High Performance Computing &Amp; Simulation (HPCS)

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“…The alternative formulation uses only the NOT, AND, and XOR operators instead. Lists of Boolean expressions of even number 1-D 3-site CA rules based on this formulation can be found in [9]. Using these operators, Rule30 can also be represented as s(j ; t)=s(j 0 1; t 0 1) 8 s(j ; t 0 1) 8 ( s(j ; t 0 1) 3 s(j +1;t 0 1)) (3) where 8 denotes the XOR operator.…”

Section: A Boolean Form Of Ca Rulesmentioning

confidence: 99%

“…Hence a set of models which are over-specified on both the spatial and temporal spans will be introduced as the model set. For a 3-D CA, the model set can be defined as s(i; j; l; t)=f (s(i + i1;j + j1;l+ l1; t 0 1); ...; s(i 0 i 2 ;j 0 j 2 ;l0 l 2 ; t 0 1);...; s(i + i1;j + j1;l+ l1; t 0 h); ...; s(i 0 i 2 ;j 0 j 2 ;l0 l 2 ; t 0 h)) (8) into the polynomial form shown in (6) yields s(i; j; l; t)= 1 u 1 + 111+ n u n + 111+ N u 1 21112u n (9) where N =2 n 0 1, and 1; ...;N are a set of integers such that (9) maps s(i; j; l; t) into f0; 1g. Note that (9) can be readily extended from the 3-D case to be valid for all binary CAs.…”

Section: Identification Using Ca-olsmentioning

confidence: 99%

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Identification of the neighborhood and CA rules from spatio-temporal CA patterns

Billings

Yang

2003

IEEE Trans. Syst., Man, Cybern. B

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Abstract-Extracting the rules from spatio-temporal patterns generated by the evolution of cellular automata (CA) usually produces a CA rule table without providing a clear understanding of the structure of the neighborhood or the CA rule. In this paper, a new identification method based on using a modified orthogonal least squares or CA-OLS algorithm to detect the neighborhood structure and the underlying polynomial form of the CA rules is proposed. The Quine-McCluskey method is then applied to extract minimum Boolean expressions from the polynomials. Spatio-temporal patterns produced by the evolution of one-dimensional (1-D), two-dimensional (2-D), and higher dimensional binary CAs are used to illustrate the new algorithm and simulation results show that the CA-OLS algorithm can quickly select both the correct neighborhood structure and the corresponding rule.

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Books received

2000

Complexity

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As paradigmatic complex systems, various studies have been done in the context of one-dimensional cellular automata (CA) on the definition of parameters directly obtained from their transition rule, aiming at the help they might provide to forecasting CA dynamic behavior. Out of the analysis of the most important parameters available for this end, as well as others evaluated by us, a set of guidelines is proposed that should be followed when defining a parameter of that kind. Based upon the guidelines, a critique of those parameters is made, which leads to a set of five that jointly provide a good forecasting set; two of them were drawn from the literature and three are new ones defined according to the guidelines. By using them as a heuristic in the evolutionary search for CA of a predefined computational behavior, good results have been obtained, exemplified herein by the evolutionary search for CA that perform the Synchronization Task. ᭧ 2001 John Wiley & Sons, Inc. SUMMARY C ellular automata (CA) are discrete complex systems which possess both a dynamic and a computational nature. In either case, based only upon their definition, it is not possible to forecast either their dynamic behavior, or the computation they will perform when running. However, it is possible to derive static parameters from their definition, which can then be used to estimate their dynamic behavior. This has already been done in the literature, but here we significantly extend previous efforts, by means of an analysis of the available parameters and the definition of new ones, which is achieved through the identification of a set of guidelines those parameters should abide by. The effectiveness of these guidelines are demonstrated, by using a set of five parameters drawn from them, as aids in the design of CA that should perform a predefined computational task; in the current case, such an aid represents guiding an evolutionary search for CA that perform a well-known task for one-dimensional CA, the so-called Synchronization Task.

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Computational Analysis of One-Dimensional Cellular Automata

Cited by 16 publications

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

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

Identification of the neighborhood and CA rules from spatio-temporal CA patterns

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