Probability of State Transition Errors in a Finite State Machine Containing Soft Failures

A Markov model of a finite state machine realization containing gates and memory elements each subject to internal soft errors is given and a computational method for determining the probability of state transition errors is presented. The system inputs are taken as stochasticaily driven and the long-run stationary probability distribution of the states is developed. Similar results are determined for a fault-tolerant realization using error-correcting codes to form cluster states according to a technique of Reed. The state transition error performance of the coded machine is compared to that of the original realization; a dramatic improvement is seen when normally small soft error rates are encountered. The computational aspects of the required probabilities are investigated and a simplified approximation approach is proposed and analyzed. Bounds on the approximation inaccuracies are derived.