Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems
- Cite this paper as:
- 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
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.