English

Senescent Ground Tree Rewrite Systems

Formal Languages and Automata Theory 2013-11-21 v1 Logic in Computer Science

Abstract

Ground Tree Rewrite Systems with State are known to have an undecidable control state reachability problem. Taking inspiration from the recent introduction of scope-bounded multi-stack pushdown systems, we define Senescent Ground Tree Rewrite Systems. These are a restriction of ground tree rewrite systems with state such that nodes of the tree may no longer be rewritten after having witnessed an a priori fixed number of control state changes. As well as generalising scope-bounded multi-stack pushdown systems, we show --- via reductions to and from reset Petri-nets --- that these systems have an Ackermann-complete control state reachability problem. However, reachability of a regular set of trees remains undecidable.

Cite

@article{arxiv.1311.4915,
  title  = {Senescent Ground Tree Rewrite Systems},
  author = {Matthew Hague},
  journal= {arXiv preprint arXiv:1311.4915},
  year   = {2013}
}
R2 v1 2026-06-22T02:10:52.389Z