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Size of reversible circuits as a measure of even permutation complexity

Authors: Zakablukov D.V. Published: 08.02.2015
Published in issue: #1(100)/2015  
DOI: 10.18698/0236-3933-2015-1-67-82

 
Category: Informatics, Computer Engineering and Control | Chapter: Theoretical Computer Science, Cybernetics  
Keywords: reversible circuits, gate complexity, even permutation complexity

The article considers even permutation complexity by estimating the size of reversible circuits composed of NOT, CNOT and 2-CNOT gates implementing these permutations. It is proved that every even permutation of Zn2 set can be implemented by a reversible circuit with the gate complexity equivalent up to about n2n/log2n order, without the use of additional inputs; all other even permutations can be implemented by reversible circuit with less gate complexity, without the use of additional inputs. It is established that every even permutation of Zn2 set can be implemented by a reversible circuit with < 2n+1 gate complexity, using ~ 5 • 2n/n additional inputs. For every even permutation usage of additional inputs allows decreasing the gate complexity of reversible circuits by implementing them.

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