Probabilistic Complexity Classes through Semantics
Computational Complexity
2020-02-04 v1 Logic in Computer Science
Dynamical Systems
Logic
Abstract
In a recent paper, the author has shown how Interaction Graphs models for linear logic can be used to obtain implicit characterisations of non-deterministic complexity classes. In this paper, we show how this semantic approach to Implicit Complexity Theory (ICC) can be used to characterise deterministic and probabilistic models of computation. In doing so, we obtain correspondences between group actions and both deterministic and probabilistic hierarchies of complexity classes. As a particular case, we provide the first implicit characterisations of the classes PLogspace (un-bounded error probabilistic logarithmic space) and PPtime (unbounded error probabilistic polynomial time)
Cite
@article{arxiv.2002.00009,
title = {Probabilistic Complexity Classes through Semantics},
author = {Thomas Seiller},
journal= {arXiv preprint arXiv:2002.00009},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1609.07895