English

The First-Order Theory of Ground Tree Rewrite Graphs

Logic in Computer Science 2015-07-01 v4 Computational Complexity

Abstract

We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.

Keywords

Cite

@article{arxiv.1107.0919,
  title  = {The First-Order Theory of Ground Tree Rewrite Graphs},
  author = {Stefan Göller and Markus Lohrey},
  journal= {arXiv preprint arXiv:1107.0919},
  year   = {2015}
}

Comments

accepted for Logical Methods in Computer Science