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Self-Inverse Functions and Palindromic Circuits
We investigate the subclass of reversible functions that are self-inverse and
relate them to reversible circuits that are equal to their reverse circuit,
which are called palindromic circuits. We precisely determine which
self-inverse functions can be realized as a palindromic circuit. For those
functions that cannot be realized as a palindromic circuit, we find alternative
palindromic representations that require an extra circuit line or quantum gates
in their construction. Our analyses make use of involutions in the symmetric
group which are isomorphic to self-inverse reversible function on
variables.Comment: 6 pages, 3 figure