2 research outputs found
Choiceless Polynomial Time with Witnessed Symmetric Choice
We extend Choiceless Polynomial Time (CPT), the currently only remaining
promising candidate in the quest for a logic capturing PTime, so that this
extended logic has the following property: for every class of structures for
which isomorphism is definable, the logic automatically captures PTime.
For the construction of this logic we extend CPT by a witnessed symmetric
choice operator. This operator allows for choices from definable orbits. But,
to ensure polynomial time evaluation, automorphisms have to be provided to
certify that the choice set is indeed an orbit.
We argue that, in this logic, definable isomorphism implies definable
canonization. Thereby, our construction removes the non-trivial step of
extending isomorphism definability results to canonization. This step was a
part of proofs that show that CPT or other logics capture PTime on a particular
class of structures. The step typically required substantial extra effort.Comment: 65 pages. Full version of a paper to appear at LICS 22. v2: corrected
typos and small mistake