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arXiv · 1311.4915

Senescent Ground Tree Rewrite Systems

Matthew Hague
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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.

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Matthew Hague. 2013-11-19. Senescent Ground Tree Rewrite Systems. https://arxiv.org/abs/1311.4915

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