Log-trimmable subgroup description rule

Definition
A subgroup description rule is said to be log-trimmable if there is an algorithm that, given any log-size encoding of a group, and a description of a subgroup using the subgroup description rule, outputs a description of the subgroup that is polynomial in the log-size, such that the time taken by the algorithm is bounded by a polynomial in the log-size and in the size of the original subgroup description.

Weaker properties

 * Log-size subgroup description rule