ar X iv : 1 50 2 . 05 87 3 v 2 [ cs . F L ] 2 5 Fe b 20 15 Annotated Stack Trees ∗
نویسنده
چکیده
Annotated pushdown automata provide an automaton model of higher-order recursion schemes, which may in turn be used to model higher-order programs for the purposes of verification. We study Ground Annotated Stack Tree Rewrite Systems – a tree rewrite system where each node is labelled by the configuration of an annotated pushdown automaton. This allows the modelling of fork and join constructs in higher-order programs and is a generalisation of higher-order stack trees recently introduced by Penelle. We show that, given a regular set of annotated stack trees, the set of trees that can reach this set is also regular, and constructible in n-EXPTIME for an order-n system, which is optimal. We also show that our construction can be extended to allow a global state through which unrelated nodes of the tree may communicate, provided the number of communications is subject to a fixed bound.
منابع مشابه
ar X iv : 1 50 2 . 04 65 3 v 1 [ cs . F L ] 1 6 Fe b 20 15 Rewriting Higher - Order Stack Trees ⋆
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 ...
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