Matthew Hague ; C. -H. Luke Ong - Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems

lmcs:831 - Logical Methods in Computer Science, December 5, 2008, Volume 4, Issue 4 -
Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems

Authors: Matthew Hague ; C. -H. Luke Ong

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.

Volume: Volume 4, Issue 4
Published on: December 5, 2008
Accepted on: June 25, 2015
Submitted on: September 26, 2007
Keywords: Computer Science - Computational Complexity,Computer Science - Computer Science and Game Theory,F.1.1


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