First-Order Model Checking on Generalisations of Pushdown Graphs

First-Order Model Checking on Generalisations of Pushdown Graphs

A First-Order Logic on Higher-Order Nested Pushdown Trees

We introduce a new hierarchy of higher-order nested pushdown trees generalising Alur et al.’s concept of nested pushdown trees. Nested pushdown trees are useful representations of control flows in the verification of programs with recursive calls of first-order functions. Higher-order nested pushdown trees are expansions of unfoldings of graphs generated by higher-order pushdown systems. Moreov...

FO Model Checking on Nested Pushdown Trees

Nested Pushdown Trees are unfoldings of pushdown graphs with an additional jump-relation. These graphs are closely related to collapsible pushdown graphs. They enjoy decidable μ-calculus model checking while monadic second-order logic is undecidable on this class. We show that nested pushdown trees are tree-automatic structures, whence first-ordermodel checking is decidable. Furthermore, we pro...

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 ...

The Complexity of Games on Higher Order Pushdown Automata

We prove an n-exptime lower bound for the problem of deciding the winner in a reachability game on Higher Order Pushdown Automata (HPDA) of level n. This bound matches the known upper bound for parity games on HPDA. As a consequence the μ-calculus model checking over graphs given by n-HPDA is n-exptime complete.