Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems

Matthew Hague; C. -H. Luke Ong

doi:10.2168/lmcs-4(4:14)2008

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arXiv · 0811.1103

Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems

Matthew Hague·C. -H. Luke Ong

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Abstract

Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure. These systems may be used to model higher-order programs and are closely related to the Caucal hierarchy of infinite graphs and safe higher-order recursion schemes. We consider the backwards-reachability problem over higher-order Alternating PDSs (APDSs), a generalisation of higher-order PDSs. This builds on and extends previous work on pushdown systems and context-free higher-order processes in a non-trivial manner. In particular, we show that the set of configurations from which a regular set of higher-order APDS configurations is reachable is regular and computable in n-EXPTIME. In fact, the problem is n-EXPTIME-complete. We show that this work has several applications in the verification of higher-order PDSs, such as linear-time model-checking, alternation-free mu-calculus model-checking and the computation of winning regions of reachability games.

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Matthew Hague, C. -H. Luke Ong. 2008-11-07. Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems. https://doi.org/10.2168/lmcs-4(4%3A14)2008

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