Witnessed symmetric choice is an extension of choiceless polynomial time with counting that permits choosing an element of an orbit while constructing automorphisms certifying the symmetry of the choice set. The witnessing automorphisms preserve the entire input vocabulary and stabilize both parameters and preceding intermediate states. This restriction allows intermediate choices while preserving invariance under renaming the input elements.
Witnessed Symmetric Choice
See also
Choiceless Polynomial Time with Counting, Group Action, Polynomial TimeExplore with Wolfram|Alpha
References
Lichter, M. and Schweitzer, P. "Choiceless Polynomial Time with Witnessed Symmetric Choice." J. ACM 71, Article 7, 1-70, 2024. https://doi.org/10.1145/3648104.Cite this as:
Weisstein, Eric W. "Witnessed Symmetric Choice." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WitnessedSymmetricChoice.html