Fault Tolerance in Cellular Automata at Low Fault Rates

TL;DR

This paper investigates the fault tolerance of two-dimensional cellular automata, classifying tessellations based on their ability to withstand low fault rates under different fault models, including transient and manufacturing faults.

Contribution

It provides a complete classification of regular tessellations regarding their fault tolerance under combined and separate fault models.

Findings

Certain tessellations can tolerate low fault rates with majority voting.

Classification of tessellations into fault-tolerant and non-fault-tolerant categories.

Analysis includes both transient and manufacturing fault models.

Abstract

A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the case we treat in this paper. The conceptually simplest mechanism for correcting errors in a cellular automaton is to determine the next state of a cell by taking a majority vote among its neighbors (including the cell itself, if necessary to break ties). We are interested in which regular two-dimensional tessellations can tolerate faults using this mechanism, when the fault rate is sufficiently low. We consider both the traditional transient fault model (where faults occur independently in time and space) and a recently introduced combined fault model which also includes manufacturing faults (which occur independently in space, but which affect cells for all time). We completely classify regular two-dimensional tessellations as to whether they can tolerate combined transient and manufacturing faults, transient faults but not manufacturing faults, or not even transient faults.