Complete Simulation of Automata Networks

Bridoux, Florian; Castillo-Ramirez, Alonso; Gadouleau, Maximilien

Abstract

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.

Citation

Bridoux, F., Castillo-Ramirez, A., & Gadouleau, M. (2020). Complete Simulation of Automata Networks. Journal of Computer and System Sciences, 109, 1-21. https://doi.org/10.1016/j.jcss.2019.12.001

• Journal Article Type: Article
• Acceptance Date: Dec 1, 2019
• Online Publication Date: Dec 6, 2019
• Publication Date: May 31, 2020
• Deposit Date: Dec 10, 2019
• Publicly Available Date: Dec 6, 2020
• Journal: Journal of Computer and System Sciences
• Print ISSN: 0022-0000
• Electronic ISSN: 1090-2724
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 109
• Pages: 1-21
• DOI: https://doi.org/10.1016/j.jcss.2019.12.001
• Public URL: https://durham-repository.worktribe.com/output/1275768