Papers › Choiceless polynomial time
Choiceless polynomial time
Andreas Blass, Yuri Gurevich, Saharon Shelah
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be recast as follows: Does there exist a logic that captures polynomial time (without presuming the presence of a linear order)? Earlier, one of us conjectured the negative answer. The problem motivated a quest for stronger and stronger PTime logics. All these logics avoid arbitrary choice. Here we attempt to capture the choiceless fragment of PTime. Our computation model is a version of abstract state machines (formerly called evolving algebras). The idea is to replace arbitrary choice with parallel execution. The resulting logic is more expressive than other PTime logics in the literature. A more difficult theorem shows that the logic does not capture all PTime.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections