Hardening reliability-critical gates in a circuit is an important step to improve the circuit reliability at a low cost. However, accurately locating the reliability-critical gates is a key prerequisite for the efficient implementation of the hardening operation. In this paper, a probabilistic-based calculation method developed for locating the reliability-critical gates in a circuit is described. The proposed method is based on the generation of input vectors and the sampling of reliability-critical gates using uniform non-Bernoulli sequences, and the criticality of the gate reliability is measured by combining the structure information of the circuit itself. Both the accuracy and the efficiency of the proposed method have been illustrated by various simulations on benchmark circuits. The results show that the proposed method has an efficient performance in locating accuracy and algorithm runtime.

The reliability allowance of circuits tends to decrease with the increase of circuit integration and the application of new technology and materials, and the hardening strategy oriented toward gates is an effective technology for improving the circuit reliability of the current situations. Therefore, a parallel-structured genetic algorithm (GA), PGA, is proposed in this paper to locate reliability-critical gates to successfully perform targeted hardening. Firstly, we design a binary coding method for reliability-critical gates and build an ordered initial population consisting of dominant individuals to improve the quality of the initial population. Secondly, we construct an embedded parallel operation loop for directional crossover and directional mutation to compensate for the deficiency of the poor local search of the GA. Thirdly, for combination with a diversity protection strategy for the population, we design an elitism retention based selection method to boost the convergence speed and avoid being trapped by a local optimum. Finally, we present an ordered identification method oriented toward reliability-critical gates using a scoring mechanism to retain the potential optimal solutions in each round to improve the robustness of the proposed locating method. The simulation results on benchmark circuits show that the proposed method PGA is an efficient locating method for reliability-critical gates in terms of accuracy and convergence speed.