Abstract
Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested “stack of stacks” structure. We further generalise higher-order PDSs to higher-order Alternating PDSs (APDSs) and consider the backwards reachability problem over these systems. We prove that given an order-n APDS, the set of configurations from which a given regular set of configurations is reachable is itself regular and computable in n-EXPTIME. We show that the result has several useful applications in the verification of higher-order PDSs such as LTL model checking, alternation-free μ-calculus model checking, and the computation of winning regions of reachability games.
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Hague, M., Ong, C.H.L. (2007). Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems. In: Seidl, H. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2007. Lecture Notes in Computer Science, vol 4423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71389-0_16
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