It is well-known that every permutation can be written as the composition of two involutions.

Suppose that $p$ is a polynomial. Then does there exist a polynomial $q$ such that if $f:\{0,1\}^{n}\rightarrow\{0,1\}^{n}$ and its inverse are permutations which are computable by combinatorial circuits with at most $p(n)$ gates, then there exists involutions $g,h:\{0,1\}^{n}\rightarrow\{0,1\}^{n}$ such that $f=g\circ h$ and where $g,h$ are computable by a combinatorial circuit with at most $q(n)$ gates?


Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.