Computation by asynchronously updating cellular automata

Implementations of synchronous updating can be analysed in two phases.

The first, interaction, calculates the new state of each cell based on the neighbourhood and the update rule. The second phase updates state values by copying the new states to the cells.

Springer, Berlin, Heidelberg There is increasing interest in cellular automata that update their cells asynchronously, i.e., at random times and independent of each other.

A known method to compute on an asynchronously updating cellular automaton is the simulation of a synchronous computing model on it.

The state of every cell in the model is updated together, before any of the new states influence other cells.

In contrast, an asynchronous cellular automaton is able to update individual cells independently, in such a way that the new state of a cell affects the calculation of states in neighbouring cells.

This paper employs local synchronization, a technique in which particular temporal sequences of states are imposed locally on cells and their direct neighbors, while the exact timing of state transitions is left undetermined.

The synchronous approach assumes the presence of a global clock to ensure all cells are updated together. Nehaniv in 1998) allows one to emulate exactly the behaviour of a synchronous cellular automaton via an asynchronous one constructed as a simple modification of the synchronous cellular automaton (Nehaniv 2002).

Cellular automata have recently been proposed as an architecture for dense, locally-interacting arrays of submicron devices.

However, because conventional von Neumann cellular automata do not correctly reflect the long-range behavior of typical inter-device interactions, they do not provide a suitable theoretical model for the proposed device arrays.

This is achieved by simulating delay insensitive circuits on it, a type of asynchronous circuit that is known for its robustness to variations in the timing of signals.

Cellular automata, as with other multi-agent system models, usually treat time as discrete and state updates as occurring synchronously.