Formalization of Asynchronous Cellular Automata Using Asynchronous Protocol for Communications

Asynchronous cellular automata (ACAs) allow cells to change their states independently at random times. Nevertheless, whenever a cell is activated for state transition, its new state is decided by the state of the cell itself, together with the current states of all neighboring cells. This implies that the cell, from being activated till undergoing a transition, must access every neighbor to acquire their present states and complete all communications in due time. In this paper, we formalize a novel type of ACAs which use asynchronous communicating protocol to exchange states between neighboring cells. This enables a cell in the ACA to change the state based on some preceding states, rather than the current states, of each neighboring cell.