Do There Exist Non-linear Maximal Length Cellular Automata? A Study

Adak, Sumit; Mukherjee, Soumava; Das, Sukanta

doi:10.1007/978-3-319-99813-8_26

Cited by 6 publications

(6 citation statements)

References 5 publications

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“…In this section, we discuss a technique to generate CAs with limited number of cycles, that is, configurations are to be placed on the same cycle. This requirement matches with an existing problem statement, generation of large cycle CA, already studied in [1]. For ease of understanding, we briefly recall the idea.…”

Section: Designing Ca With Optimal Number Of Clustersmentioning

confidence: 77%

“…(Here, n is determined based on the number of features owned by the target objects which is always finite.) For ensuring that this CA has limited number of cycles, we use the framework of a related problem -CA with large cycles (introduced in [1]). However, to guarantee that for the candidate CA, the configurations inside a cycle maintain minimum possible hamming distance (as binary CA is considered for this research), we propose a scheme to select significant rules which contribute minimum change in cell's state value when transition occurs between configurations (Section 3.2).…”

Section: Introductionmentioning

confidence: 99%

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Cycle Based Clustering Using Reversible Cellular Automata

Mukherjee

Bhattacharjee

Das

2020

Lecture Notes in Computer Science

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This work proposes cycle based clustering technique using reversible cellular automata (CAs) where 'closeness' among objects is represented as objects belonging to the same cycle, that is reachable from each other. The properties of such CAs are exploited for grouping the objects with minimum intra-cluster distance while ensuring that limited number of cycles exist in the configuration-space. The proposed algorithm follows an iterative strategy where the clusters with closely reachable objects of previous level are merged in the present level using an unique auxiliary CA. Finally, it is observed that, our algorithm is at least at par with the best algorithm existing today.

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Section: Designing Ca With Optimal Number Of Clustersmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Cycle Based Clustering Using Reversible Cellular Automata

Mukherjee

Bhattacharjee

Das

2020

Lecture Notes in Computer Science

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“…for CA (60) all cycles already found for the factors CA (4,5,10,12,15,20,30) have to be included. We can summarize that for n ≤ 60, the longest paths are much smaller than 2 n − 1 (which is achievable with other ECA rules [21]). Further work remains to find a general formula or at least boundaries for the longest paths and the cycle distribution, depending on a number of cells.…”

Section: Longest Paths and Representative Cyclesmentioning

confidence: 81%

On Patterns and Dynamics of Rule 22 Cellular Automaton

Mart́ınez¹,

Adamatzky²,

Hoffmann³

et al. 2019

ComplexSystems

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Rule 22 elementary cellular automaton (ECA) has a 3-cell neighborhood, binary cell states, where a cell takes state '1' if there is exactly one neighbor, including the cell itself, in state '1'. In Boolean terms the cellstate transition is a xor function of three cell states. In physico-chemical terms the rule might be seen as describing propagation of self-inhibiting quantities/species. Space-time dynamics of Rule 22 demonstrates nontrivial patterns and quasi-chaotic behavior. We characterize the phenomena observed in this rule using mean field theory, attractors, de Bruijn diagrams, subset diagrams, filters, fractals and memory.

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“…The paper [5], for example, investigates the maximal length of temporal periods of binary CA under null boundary condition, and demonstrates that the maximal length 2 σ − 1 can be obtained by additive rules, for any σ > 0. In [1], the authors address the same question for non-additive CA, and show that the maximal length can also be obtained, if the rule is allowed to be non-uniform among sites. Works that investigate additive rules and their temporal periods also include [10], [16], [17], and [15].…”

Section: Introductionmentioning

confidence: 98%

“…It is clear that min f Y σ,n (f ) = min f X σ,n (f ) = 1, as the minima are attained by the identity n-state rule, i.e., the rule f given by f (c 0 , c 1 ) = c 1 , for all c 0 , c 1 ∈ Z n . We therefore focus on (1)…”

Section: Introductionmentioning

confidence: 99%

Maximal temporal period of a periodic solution generated by a one-dimensional cellular automaton

Gravner¹,

Liu²

2019

Preprint

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We study one-dimensional cellular automata evolutions with both temporal and spatial periodicity. The main objective is to investigate the longest temporal periods among all two-neighbor rules, with a fixed spatial period σ and number of states n. When σ = 2, 3, 4, or 6, and we restrict the rules to be additive, the longest period can be expressed as the exponent of the multiplicative group of an appropriate ring. We also construct non-additive rules with temporal period on the same order as the trivial upper bound n σ . Experimental results, open problems, and possible extensions of our results are also discussed.

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Do There Exist Non-linear Maximal Length Cellular Automata? A Study

Cited by 6 publications

References 5 publications

Cycle Based Clustering Using Reversible Cellular Automata

Cycle Based Clustering Using Reversible Cellular Automata

On Patterns and Dynamics of Rule 22 Cellular Automaton

Maximal temporal period of a periodic solution generated by a one-dimensional cellular automaton

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