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arXiv · 1502.04653

Rewriting Higher-Order Stack Trees

Vincent Penelle
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Abstract

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. Indeed, the model-checking problem for monadic second order logic (respectively 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.

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Vincent Penelle. 2015-02-16. Rewriting Higher-Order Stack Trees. https://arxiv.org/abs/1502.04653

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