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Rewriting Higher-Order Stack Trees

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. 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.
Keywords : stack trees
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Submitted on : Tuesday, September 15, 2015 - 3:39:56 PM
Last modification on : Saturday, January 15, 2022 - 3:58:07 AM
Long-term archiving on: : Wednesday, April 26, 2017 - 6:33:19 PM


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Vincent Penelle. Rewriting Higher-Order Stack Trees. CSR 2015, Jul 2015, Listvyanka, Russia. pp.364-397, ⟨10.1007/978-3-319-20297-6_24⟩. ⟨hal-01117753v2⟩



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