FPGA fabric conscious architecture design and automation of speed-area efficient Margolus neighborhood based cellular automata with variegated scan path insertion

Palchaudhuri, Ayan; Anand, Digvijay; Dhar, Anindya Sundar

doi:10.1016/j.jpdc.2022.04.020

Cited by 2 publications

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The attractive feature of CA is that contemporary algorithms of parallel computing can be naturally embedded in them. Various cellular algorithms were successfully implemented on field-programmable gate arrays (FPGA) [2,3] and on graphic cards [4,5].…”

Section: Introductionmentioning

confidence: 99%

Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain

Kulagin

Шаповалов

2023

Mathematics

View full text Add to dashboard Cite

The one-parameter two-dimensional cellular automaton with the Margolus neighbourhood is analyzed based on considering the projection of the stochastic movements of a single particle. Introducing the auxiliary random variable associated with the direction of the movement, we reduce the problem under consideration to the study of a two-dimensional Markov chain. The master equation for the probability distribution is derived and solved exactly using the probability-generating function method. The probability distribution is expressed analytically in terms of Jacobi polynomials. The moments of the obtained solution allowed us to derive the exact analytical formula for the parametric dependence of the diffusion coefficient in the two-dimensional cellular automaton with the Margolus neighbourhood. Our analytic results agree with earlier empirical results of other authors and refine them. The results are of interest for the modelling two-dimensional diffusion using cellular automata especially for the multicomponent problem.

show abstract

Section: Introductionmentioning

confidence: 99%

Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain

Kulagin

Шаповалов

2023

Mathematics

View full text Add to dashboard Cite

show abstract

Analytical description of the diffusion in a cellular automaton with the Margolus neighbourhood in terms of the two-dimensional Markov chain

Kulagin¹,

Шаповалов²

2022

Preprint

View full text Add to dashboard Cite

The one-parameter two-dimensional cellular automaton with the Margolus neighbourhood is analyzed based on the considering the projection of the stochastic movements of a single particle.Introducing the auxiliary random variable associated with the direction of the movement, we reduce the problem under consideration to the study of a two-dimensional Markov chain. The master equation for the probability distribution is derived and solved exactly using the probability generating function method. The probability distribution is expressed analytically in terms of Jacobi polynomials. The moments of the obtained solution allowed us to derive the exact analytical formula for the parametric dependence of the diffusion coefficient in the two-dimensional cellular automaton with the Margolus neighbourhood. Our analytic results agree with earlier empirical results of other authors and refine them. The results are of interest for the modelling two-dimensional diffusion using cellular automata especially for the multicomponent problem.

show abstract

FPGA fabric conscious architecture design and automation of speed-area efficient Margolus neighborhood based cellular automata with variegated scan path insertion

Cited by 2 publications

References 15 publications

Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain

Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain

Analytical description of the diffusion in a cellular automaton with the Margolus neighbourhood in terms of the two-dimensional Markov chain

Contact Info

Product

Resources

About