## JMI2010A-6 Abstract collision systems on $G$-sets (pp.57-73)

Author(s)： Takahiro Ito

J. Math-for-Ind. 2A (2010) 57-73.

Abstract
In this paper, we discuss an abstract collision system (ACS) on a $G$-set which is an extension of a normal ACS [5, 6]. An ACS is a type of unconventional computing framework that includes collision-based computing, cellular automata (CA), and chemical reaction systems. For a given group $G$ and its subset, we create a set of collisions and a local transition function of an ACS by using the action of $G$. We first refine definitions of the components of an ACS, and then extend them to the concepts on a $G$-set. Finally, we define and investigate the operations "union", "division" and "composition" of the ACS on a $G$-set.

Keyword(s).　 collision-based computing, cellular automata