Rewriting Higher-Order Stack Trees

Systèmes de réécriture d’arbres de piles

Vincent Penelle (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. In-deed, the model-checking problem for monadic second order logic (re-spectively first order logic with a reachability predicate) is decidable on such graphs. We unify both models by introducing the notion of stack trees, trees whose nodes are labelled by higher-order stacks, and define the corresponding class of higher-order ground tree rewriting systems. We show that these graphs retain the decidability properties of ground tree rewriting graphs while generalising the pushdown hierarchy of graphs.

Domaines: Théorie et langage formel [cs.FL]

Vincent Penelle. Rewriting Higher-Order Stack Trees. 2014. ⟨hal-01117753v1⟩