We examine the gate complexity of reversible circuits without additional inputs.
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We examine the depth of reversible circuits without additional inputs.
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Lower asymptotic bounds for the gate complexity and the depth are proved.
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New group theory based synthesis algorithm of reversible circuits is proposed.
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Upper asymptotic bounds for the gate complexity and the depth are proved.
Abstract
In the paper we study reversible logic circuits, which consist of NOT, CNOT and C2NOT gates. We consider a set of all transformations that can be realized by reversible circuits with inputs. We define the Shannon gate complexity function and the depth function as functions of n and the number of additional inputs q. We prove general lower bounds for these functions. We introduce a new group-theory-based synthesis algorithm that can produce a reversible circuit without additional inputs and with the gate complexity in the worst case.