Complexity Analysis of Tree Share Structure
Abstract
The tree share structure proposed by Dockins et al. is an elegant model for tracking disjoint ownership in concurrent separation logic, but decision procedures for tree shares are hard to implement due to a lack of a systematic theoretical study. We show that the first-order theory of the full Boolean algebra of tree shares (that is, with all tree-share constants) is decidable and has the same complexity as of the first-order theory of Countable Atomless Boolean Algebras. We prove that combining this additive structure with a constant-restricted unary multiplicative "relativization" operator has a non-elementary lower bound. We examine the consequences of this lower bound and prove that it comes from the combination of both theories by proving an upper bound on a generalization of the restricted multiplicative theory in isolation.
Cite
@article{arxiv.2010.02340,
title = {Complexity Analysis of Tree Share Structure},
author = {Xuan-Bach Le and Aquinas Hobor and Anthony W. Lin},
journal= {arXiv preprint arXiv:2010.02340},
year = {2020}
}
Comments
20 pages including appendix. Published at the 16th Asian Symposium on Programming Languages and Systems (APLAS 2018) in December 2018