Linear-Time Recognition of Connectivity of Binary Images on 1-bit Inter-Cell Communication Cellular Automata and Their Related Algorithms

1998 ◽  
pp. 139-145
Author(s):  
Hiroshi Umeo
Keyword(s):  
Cellular Automata ◽  
Linear Time ◽  
Cell Communication ◽  
Binary Images

Automatic Texture Based Classification of the Dynamics of One-Dimensional Binary Cellular Automata

2019 ◽  
Vol 8 (4) ◽  
pp. 41-61
Author(s):  
Marcelo Arbori Nogueira ◽  
Pedro Paulo Balbi de Oliveira
Keyword(s):  
Cellular Automata ◽  
Dynamic Behavior ◽  
Temporal Evolution ◽  
Computational Cost ◽  
Great Variability ◽  
Texture Descriptor ◽  
One Dimensional ◽  
Binary Images ◽  
Elementary Cellular Automata

Cellular automata present great variability in their temporal evolutions due to the number of rules and initial configurations. The possibility of automatically classifying its dynamic behavior would be of great value when studying properties of its dynamics. By counting on elementary cellular automata, and considering its temporal evolution as binary images, the authors created a texture descriptor of the images - based on the neighborhood configurations of the cells in temporal evolutions - so that it could be associated to each dynamic behavior class, following the scheme of Wolfram's classic classification. It was then possible to predict the class of rules of a temporal evolution of an elementary rule in a more effective way than others in the literature in terms of precision and computational cost. By applying the classifier to the larger neighborhood space containing 4 cells, accuracy decreased to just over 70%. However, the classifier is still able to provide some information about the dynamics of an unknown larger space with reduced computational cost.

Local Data Flow Principles in Porosity of Materials

2015 ◽  
Vol 725-726 ◽  
pp. 371-376 ◽  
Author(s):  
Biljana Stamatovic ◽  
Artem Korsun
Keyword(s):  
Cellular Automata ◽  
Porous Materials ◽  
Data Flow ◽  
Parallel Computer ◽  
Local Data ◽  
Initial Image ◽  
Binary Images ◽  
Closed Pore ◽  
Arbitrary Shapes

We propose a new algorithm for counting closed pores in porous materials. Closed pore can be defined as isolated object of arbitrary shapes in rectangular domains or binary images. The algorithm is based on two cellular automata (CA). First CA saves 2 or more connectivity of image while the second CA is Leviald’s CA that count 1-connected parts after transformations of the initial image. The CA algorithm was implemented on a parallel computer. Computational performances are evaluated and measured on real cases. The obtained results indicate that the proposed approach achieves comparable complexity as standard approaches; however, the number of processing nodes does not limit the speedup and scalability of the proposed algorithm.

scholarly journals Number conserving cellular automata: new results on decidability and dynamics

2003 ◽  
Vol DMTCS Proceedings vol. AB,... (Proceedings) ◽  
Author(s):  
Bruno Durand ◽  
Enrico Formenti ◽  
Aristide Grange ◽  
Zsuzsanna Róka
Keyword(s):  
Cellular Automata ◽  
Linear Time ◽  
Number Conservation ◽  
International Audience

International audience This paper is a survey on our recent results about number conserving cellular automata. First, we prove the linear time decidability of the property of number conservation. The sequel focuses on dynamical evolutions of number conserving cellular automata.

scholarly journals Representing Reversible Cellular Automata with Reversible Block Cellular Automata

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Jérôme Durand-Lose
Keyword(s):  
System Theory ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Linear Time ◽  
Fixed Size ◽  
Mathematical System ◽  
Reversible Cellular Automaton ◽  
International Audience ◽  
Infinite Lattices ◽  
Reversible Cellular Automata

International audience Cellular automata are mappings over infinite lattices such that each cell is updated according tothe states around it and a unique local function.Block permutations are mappings that generalize a given permutation of blocks (finite arrays of fixed size) to a given partition of the lattice in blocks.We prove that any d-dimensional reversible cellular automaton can be exp ressed as thecomposition of d+1 block permutations.We built a simulation in linear time of reversible cellular automata by reversible block cellular automata (also known as partitioning CA and CA with the Margolus neighborhood) which is valid for both finite and infinite configurations. This proves a 1990 conjecture by Toffoli and Margolus <i>(Physica D 45)</i> improved by Kari in 1996 <i>(Mathematical System Theory 29)</i>.

Linear Time Algorithm for Identifying the Invertibility of Null-Boundary Three Neighborhood Cellular Automata

2010 ◽  
Vol 19 (1) ◽  
pp. 89-113 ◽  
Author(s):  
Nirmalya S. Maiti ◽  
Soumyabrata Ghosh ◽  
Shiladitya Munshi ◽  
P. Pal Chaudhuri ◽  
Keyword(s):  
Cellular Automata ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm

scholarly journals Iterative arrays with finite inter-cell communication

2020 ◽  
Author(s):  
Martin Kutrib ◽  
Andreas Malcher
Keyword(s):  
Cellular Automata ◽  
Cell Communication ◽  
Constant Number ◽  
Computational Capacity

Abstract Iterative arrays whose internal inter-cell communication is quantitatively restricted are investigated. The quantity of communication is measured by counting the number of uses of the links between cells. In particular, iterative arrays are studied where the maximum number of communications per cell occurring in accepting computations is drastically bounded by a constant number. Additionally, the iterative arrays have to work in realtime. We study the computational capacity of such devices. For example, a result is that a strict and dense hierarchy with respect to the constant number of communications exists. Due to their very restricted communication, the question arises whether the usually studied decidability problems such as, for example, emptiness, finiteness, inclusion, or equivalence become decidable for such devices. However, it can be shown that all such decidability questions remain undecidable even if only four communications per cell are allowed. Finally, the undecidability results are shown to hold as well for one-way and two-way cellular automata having at most four communications per cell.

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