research-article

Unboundedness and downward closures of higher-order pushdown automata

Authors:

Jonathan Kochems,

C.-H. Luke OngAuthors Info & Claims

POPL '16: Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Pages 151 - 163

https://doi.org/10.1145/2837614.2837627

Published: 11 January 2016 Publication History

Abstract

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 role in verifying concurrent higher-order programs expressed as HOPDA or safe higher-order recursion schemes.

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Cited By

Ciobanu LZetzsche GSobocinski PLago UEsparza J(2024)Slice closures of indexed languages and word equations with counting constraintsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662134(1-12)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662134
Anand ASchmitz SSchütze LZetzsche GSobocinski PLago UEsparza J(2024)Verifying Unboundedness via AmalgamationProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662133(1-15)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662133
Baumann PD’Alessandro FGanardi MIbarra OMcQuillan ISchütze LZetzsche G(2023)Unboundedness Problems for Machines with Reversal-Bounded CountersFoundations of Software Science and Computation Structures10.1007/978-3-031-30829-1_12(240-264)Online publication date: 21-Apr-2023
https://doi.org/10.1007/978-3-031-30829-1_12
Show More Cited By

Index Terms

Unboundedness and downward closures of higher-order pushdown automata
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
2. Theory of computation
  1. Formal languages and automata theory

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cover image ACM Conferences

POPL '16: Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 2016

815 pages

ISBN:9781450335492

DOI:10.1145/2837614

General Chair:
Rastislav Bodik
UC Berkeley, USA
,
Program Chair:
Rupak Majumdar
MPI-SWS, Germany

ACM SIGPLAN Notices Volume 51, Issue 1
POPL '16
January 2016
815 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2914770
Editor:
Andy Gill
University of Kansas, Lawrence, KS
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Published: 11 January 2016

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POPL '16: The 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 20 - 22, 2016

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Cited By

Ciobanu LZetzsche GSobocinski PLago UEsparza J(2024)Slice closures of indexed languages and word equations with counting constraintsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662134(1-12)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662134
Anand ASchmitz SSchütze LZetzsche GSobocinski PLago UEsparza J(2024)Verifying Unboundedness via AmalgamationProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662133(1-15)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662133
Baumann PD’Alessandro FGanardi MIbarra OMcQuillan ISchütze LZetzsche G(2023)Unboundedness Problems for Machines with Reversal-Bounded CountersFoundations of Software Science and Computation Structures10.1007/978-3-031-30829-1_12(240-264)Online publication date: 21-Apr-2023
https://doi.org/10.1007/978-3-031-30829-1_12
Zetzsche G(2018)Separability by piecewise testable languages and downward closures beyond subwordsProceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3209108.3209201(929-938)Online publication date: 9-Jul-2018
https://dl.acm.org/doi/10.1145/3209108.3209201
Hague MPenelle V(2018)Constrained Dynamic Tree NetworksReachability Problems10.1007/978-3-030-00250-3_4(45-58)Online publication date: 30-Aug-2018
https://doi.org/10.1007/978-3-030-00250-3_4
Parys P(2017)Intersection Types and CountingElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.242.6242(48-63)Online publication date: 7-Feb-2017
https://doi.org/10.4204/EPTCS.242.6
Atig MChistikov DHofman PKumar KSaivasan PZetzsche GKoskinen EGrohe MShankar N(2016)The complexity of regular abstractions of one-counter languagesProceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/2933575.2934561(207-216)Online publication date: 5-Jul-2016
https://dl.acm.org/doi/10.1145/2933575.2934561
Clemente LParys PSalvati SWalukiewicz IKoskinen EGrohe MShankar N(2016)The Diagonal Problem for Higher-Order Recursion Schemes is DecidableProceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/2933575.2934527(96-105)Online publication date: 5-Jul-2016
https://dl.acm.org/doi/10.1145/2933575.2934527
Majumdar RThinniyam RZetzsche G(2021)General Decidability Results for Asynchronous Shared-Memory Programs: Higher-Order and BeyondTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-72016-2_24(449-467)Online publication date: 20-Mar-2021
https://doi.org/10.1007/978-3-030-72016-2_24
Herrmann LVogler HDroste M(2019)Weighted automata with storageInformation and Computation10.1016/j.ic.2019.104447(104447)Online publication date: Aug-2019
https://doi.org/10.1016/j.ic.2019.104447

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