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The paper discusses the gate complexity of reversible circuits consisting ofNOT, CNOT and 2-CNOT gates. The Shannon gate complexity function $L(n, q)$ fora reversible circuit, implementing a Boolean transformation $f\colon \mathbbZ_2^n \to \mathbb Z_2^n$, is defined as a function of $n$ and the number ofadditional inputs $q$. The general lower bound $L(n,q) \geq\frac{2^n(n-2)}{3\log_2(n+q)} - \frac{n}{3}$ for the gate complexity of areversible circuit is proved. An upper bound $L(n,0) \leqslant3n2^{n+4}(1+o(1)) \mathop / \log_2n$ for the gate complexity of a reversiblecircuit without additional inputs is proved. An upper bound $L(n,q_0) \lesssim2^n$ for the gate complexity of a reversible circuit with $q_0 \simn2^{n-o(n)}$ additional inputs is proved.

On Gate Complexity of Reversible Circuits Consisting of NOT, CNOT and 2-CNOT Gates