Construction of a unified theory for cellular automata using algebraic structure of lattice

2017 Fiscal Year Final Research Report

• Project/Area Number: 26600156
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Computational science
• Research Institution: Ryukoku University
• Principal Investigator: Matsukidaira Junta 龍谷大学, 理工学部, 教授 (60231594)
• Co-Investigator(Kenkyū-buntansha): 高橋 大輔 早稲田大学, 理工学術院, 教授 (50188025)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: セルオートマトン / 超離散 / Max-Min-Plus 表現 / 保存量

Outline of Final Research Achievements

Adding the mod 2 operation to Max-Min-Plus expression, we have succeeded expressing rule 142 and 14 that have second order conserved quantities as equations. And using the equations, we have succeeded showing the phase transition of the fundamental diagram mathematically. Furthermore, we have succeeded obtaining an analytic relation for the density of the conserved quatity and flux for the models stochastic variables are introduced. We have also obtained the results for the stochastic model unifying five-neighborhood particle cellular automata and asymptotic behavior analysis for three-neighborhood three-valued cellular automata. It is expected that all these results will contribute to construction of the unified theory.

Free Research Field

応用数理