Bridoux, Florian and Castillo-Ramirez, Alonso and Gadouleau, Maximilien (2020) 'Complete simulation of automata networks.', Journal of computer and system sciences., 109 . pp. 1-21.
Consider a finite set A and . We study complete simulation of transformations of , also known as automata networks. For , a transformation of is n-complete of size m if it may simulate every transformation of by updating one register at a time. Using tools from memoryless computation, we establish that there is no n-complete transformation of size n, but there is one of size . By studying various constructions, we conjecture that the maximal time of simulation of any n-complete transformation is at least 2n. We also investigate the time and size of sequentially n-complete transformations, which may simulate every finite sequence of transformations of . Finally, we show that there is no n-complete transformation updating all registers in parallel, but there exists one updating all but one register in parallel. This illustrates the strengths and weaknesses of sequential and parallel models of computation.
|Full text:||(AM) Accepted Manuscript|
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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|Publisher Web site:||https://doi.org/10.1016/j.jcss.2019.12.001|
|Publisher statement:||© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/|
|Date accepted:||01 December 2019|
|Date deposited:||10 December 2019|
|Date of first online publication:||06 December 2019|
|Date first made open access:||06 December 2020|
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