Games on Higher Order Multi-stack Pushdown Systems

Seth, Anil

doi:10.1007/978-3-642-04420-5_19

Cited by 8 publications

(6 citation statements)

References 12 publications

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“…Furthermore, we have only shown upper-bound results. Although, in the case of phase-bounded systems, our upper-bound matches that of Seth for CPDSs without collapse [27], we do not know if it is optimal. Obtaining matching lower-bounds is thus an interesting though non-obvious problem.…”

Section: Discussionmentioning

confidence: 73%

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Saturation of Concurrent Collapsible Pushdown Systems

Hague

2013

Preprint

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Multi-stack pushdown systems are a well-studied model of concurrent computation using threads with first-order procedure calls. While, in general, reachability is undecidable, there are numerous restrictions on stack behaviour that lead to decidability. To model higher-order procedures calls, a generalisation of pushdown stacks called collapsible pushdown stacks are required. Reachability problems for multi-stack collapsible pushdown systems have been little studied. Here, we study ordered, phase-bounded and scope-bounded multi-stack collapsible pushdown systems using saturation techniques, showing decidability of control state reachability and giving a regular representation of all configurations that can reach a given control state.

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Section: Discussionmentioning

confidence: 73%

“…However concurrency for these models has been little studied. Work by Seth considers phase-bounding for CPDS without collapse [27] by reduction to a finite state parity game. Recent work by Kobayashi and Igarashi studies context-bounded recursion schemes [17].…”

Section: Introductionmentioning

confidence: 99%

Saturation of Concurrent Collapsible Pushdown Systems

Hague

2013

Preprint

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“…Finally, the case of concurrent higher-order systems has been briefly considered. Seth used saturation to show that parity games over phase-bounded higher-order pushdown systems (without collapse) are effectively solvable [42]. Recently, Hague showed that the saturation approaches for first-order phasebounded, ordered and scope-bounded pushdown systems can be adapted to solve the analogous reachability problems for collapsible pushdown systems [24].…”

Section: Ground Tree Rewrite Systems and Resourcesmentioning

confidence: 99%

Saturation algorithms for model-checking pushdown systems

Carayol¹,

Hague

2014

Electron. Proc. Theor. Comput. Sci.

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“…Recently, these results have been extended to concurrent versions of CPDA and recursion schemes (e.g. [35,25,15,32]). Many approaches rely on combining representations of the Parikh image of individual automata (e.g.…”

Section: Introductionmentioning

confidence: 99%

Unboundedness and downward closures of higher-order pushdown automata

Hague

Kochems

Ong

2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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We show the diagonal problem for higher-order pushdown automata (HOPDA), and hence the simultaneous unboundedness problem, is decidable. From recent work by Zetzsche this means that we can construct the downward closure of the set of words accepted by a given HOPDA. This also means we can construct the downward closure of the Parikh image of a HOPDA. Both of these consequences play an important rôle in verifying concurrent higher-order programs expressed as HOPDA or safe higher-order recursion schemes.

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Games on Higher Order Multi-stack Pushdown Systems

Cited by 8 publications

References 12 publications

Saturation of Concurrent Collapsible Pushdown Systems

Saturation of Concurrent Collapsible Pushdown Systems

Saturation algorithms for model-checking pushdown systems

Unboundedness and downward closures of higher-order pushdown automata

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