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We study the circuit complexity of boolean functions in a certain infinitebasis. The basis consists of all functions that take value $1$ on antichainsover the boolean cube. We prove that the circuit complexity of the parityfunction and the majority function of $n$ variables in this basis is $\lfloor\frac{n+1}{2} \rfloor$ and $\left\lfloor \frac{n}{2} \right \rfloor +1$respectively. We show that the asymptotic of the maximum complexity of$n$-variable boolean functions in this basis equals $n.$

On Circuit Complexity of Parity and Majority Functions in Antichain Basis