Deriving Approximate logic circuits for triple-modular redundancy (TMR) schemes

TMR technologies are often applied for providing reliable functioning of discrete systems. But a possibility of injection the same Trojan Circuit (TC) in each copy of a TMR scheme turns the classical TMR technology into vulnerable design. To defend TMR schemes from TC injections it is possible to apply instead of three identical circuits one of them and two approximate circuits. Unfortunately this approach originates unprotected area when one of these circuits is fault. In this paper it is proposed to derive approximate circuits on a stage of forming systems of Sums of Products (SoPs). Then the obtained system are applied for synthesis of the corresponding approximate circuit. This approach gives additional means for cutting an unprotected area in comparison with deriving approximate circuits from the given combinational circuit that is conventionally used. Algorithms of generating approximate systems of Boolean functions from the given irredundant system of SoPs are suggested and the algorithm of appreciating of the unprotected area is developed.

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