On asymptotic gate complexity and depth of reversible circuits without additional memory

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Highlights

  • We examine the gate complexity of reversible circuits without additional inputs.

  • We examine the depth of reversible circuits without additional inputs.

  • Lower asymptotic bounds for the gate complexity and the depth are proved.

  • New group theory based synthesis algorithm of reversible circuits is proposed.

  • 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 F(n,q) of all transformations BnBn that can be realized by reversible circuits with (n+q) inputs. We define the Shannon gate complexity function L(n,q) and the depth function D(n,q) 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 S without additional inputs and with the gate complexity L(S)3n2n+4(1+o(1))/log2n in the worst case.

Keywords

Reversible logic
Gate complexity
Circuit depth
Asymptotic bounds

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