Choiceless Polynomial Space
Abstract
Abstract State Machines (ASMs) provide a model of computations on structures rather than strings. Blass, Gurevich and Shelah showed that deterministic PTIME-bounded ASMs define the choiceless fragment of PTIME, but cannot capture PTIME. In this article deterministic PSPACE-bounded ASMs are introduced, and it is proven that they cannot capture PSPACE. The key for the proof is a characterisation by partial fixed-point formulae over the St\"ark/Nanchen logic for deterministic ASMs and a construction of transitive structures, in which such formulae must hold. This construction exploits that the decisive support theorem for choiceless polynomial time holds under slightly weaker assumptions.
Cite
@article{arxiv.2401.16366,
title = {Choiceless Polynomial Space},
author = {Flavio Ferrarotti and Klaus-Dieter Schewe},
journal= {arXiv preprint arXiv:2401.16366},
year = {2024}
}
Comments
12 pages. arXiv admin note: substantial text overlap with arXiv:2005.04598