Resolution of Infinite‐Loop in Hyperincursive and Nonlocal Cellular Automata: Introduction to Slime Mold Computing

How can non‐algorithmic/non‐deterministic computational syntax be computed? “The hyperincursive system” introduced by Dubois is an anticipatory system embracing the contradiction/uncertainty. Although it may provide a novel viewpoint for the understanding of complex systems, conventional digital computers cannot run faithfully as the hyperincursive computational syntax specifies, in a strict sense. Then is it an imaginary story? In this paper we try to argue that it is not. We show that a model of complex systems “Elementary Conflictable Cellular Automata (ECCA)” proposed by Aono and Gunji is embracing the hyperincursivity and the nonlocality. ECCA is based on locality‐only type settings basically as well as other CA models, and/but at the same time, each cell is required to refer to globality‐dominant regularity. Due to this contradictory locality‐globality loop, the time evolution equation specifies that the system reaches the deadlock/infinite‐loop. However, we show that there is a possibility of the resolution of these problems if the computing system has parallel and/but non‐distributed property like an amoeboid organism. This paper is an introduction to “the slime mold computing” that is an attempt to cultivate an unconventional notion of computation.