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- W4320458216 abstract "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." @default.
- W4320458216 created "2023-02-14" @default.
- W4320458216 creator A5017685495 @default.
- W4320458216 creator A5050723678 @default.
- W4320458216 date "2022-05-27" @default.
- W4320458216 modified "2023-09-29" @default.
- W4320458216 title "Choiceless Polynomial Time with Witnessed Symmetric Choice" @default.
- W4320458216 doi "https://doi.org/10.48550/arxiv.2205.14003" @default.
- W4320458216 hasPublicationYear "2022" @default.
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