Deriving approximate logic circuits for TMR technique - Matrosova, Anzhela Yu (Russian physics journal)
The Triple-Modular Redundancy (TMR) technique is one of the conventional approaches to provide reliable functioning of logic circuits. When using outsourcing, it is possible to inject a Trojan Circuit (TC) in the same line of each identical TMR module, and the TMR technique becomes vulnerable. It is necessary to withstand to vulnerability. One way of solving this problem is the application of two approximate logic circuits and one correct circuit that implements the proper functioning in the frame of the TMR technique. However, this approach, as a rule, generates an unprotected area in which a fault of one of the three circuits may be undetected. It is desirable to minimize this area. In this paper, approximate circuits are built based on deriving approximate systems of Boolean functions. These systems are then applied for an approximate circuit synthesis. The approach gives additional possibilities for cutting the unprotected area compared to the methods suggested before. Algorithms of deriving the approximate systems of the Boolean functions based on analysis of an irredundant system of sums of products (SoPs) describing the behavior of the correct circuit have been developed. The algorithm appreciating the size of the unprotected area is also given.