Article

Unsafe grammars and panic automata

Authors:

Damian Niwiński,

Paweł Urzyczyn,

Igor WalukiewiczAuthors Info & Claims

ICALP'05: Proceedings of the 32nd international conference on Automata, Languages and Programming

Pages 1450 - 1461

https://doi.org/10.1007/11523468_117

Published: 11 July 2005 Publication History

Abstract

We show that the problem of checking if an infinite tree generated by a higher-order grammar of level 2 (hyperalgebraic) satisfies a given μ-calculus formula (or, equivalently, if it is accepted by an alternating parity automaton) is decidable, actually 2-Exptime-complete. Consequently, the monadic second-order theory of any hyperalgebraic tree is decidable, so that the safety restriction can be removed from our previous decidability result. The last result has been independently obtained by Aehlig, de Miranda and Ong. Our proof goes via a characterization of possibly unsafe second-order grammars by a new variant of higher-order pushdown automata, which we call panic automata. In addition to the standard pop₁ and pop₂ operations, these automata have an option of a destructive move called panic. The model-checking problem is then reduced to the problem of deciding the winner in a parity game over a suitable 2nd order pushdown system.

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Cited By

Broadbent CCarayol AHague MMurawski AOng CSerre O(2021)Collapsible Pushdown Parity GamesACM Transactions on Computational Logic10.1145/345721422:3(1-51)Online publication date: 28-Jun-2021
https://dl.acm.org/doi/10.1145/3457214
Broadbent CCarayol AOng CSerre O(2021)Higher-order Recursion Schemes and Collapsible Pushdown Automata: Logical PropertiesACM Transactions on Computational Logic10.1145/345291722:2(1-37)Online publication date: 15-May-2021
https://dl.acm.org/doi/10.1145/3452917
Hague MMurawski AOng CSerre O(2017)Collapsible Pushdown Automata and Recursion SchemesACM Transactions on Computational Logic10.1145/309112218:3(1-42)Online publication date: 11-Aug-2017
https://dl.acm.org/doi/10.1145/3091122
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Unsafe grammars and panic automata
1. Theory of computation
  1. Formal languages and automata theory

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cover image Guide Proceedings

ICALP'05: Proceedings of the 32nd international conference on Automata, Languages and Programming

July 2005

1476 pages

ISBN:3540275800

Editors:
Luís Caires
CITI / Departamento de Informática, Universidade Nova de Lisboa, Portugal
,
Giuseppe F. Italiano
Dipartimento di Informatica, Sistemi e Produzione, Università di Roma "Tor Vergata", via del Politecnico 1, Roma, Italy
,
Luís Monteiro
Departamento de Informatica, Universidade Nova de Lisboa, via del Politecnico 1, Caparica, Portugal
,
Catuscia Palamidessi
Departamento de Informatica, Ecole Polytechnique, Rue de Saclay, Palaiseau Cedex, France
,
Moti Yung
Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, New York, France

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Fundacao para a Ciencia e Tecnologia
FCT: Foundation for Science and Technology
Centro de Lógica e Computação/IST/UTL: Centro de Lógica e Computação/IST/UTL

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 11 July 2005

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Cited By

Broadbent CCarayol AHague MMurawski AOng CSerre O(2021)Collapsible Pushdown Parity GamesACM Transactions on Computational Logic10.1145/345721422:3(1-51)Online publication date: 28-Jun-2021
https://dl.acm.org/doi/10.1145/3457214
Broadbent CCarayol AOng CSerre O(2021)Higher-order Recursion Schemes and Collapsible Pushdown Automata: Logical PropertiesACM Transactions on Computational Logic10.1145/345291722:2(1-37)Online publication date: 15-May-2021
https://dl.acm.org/doi/10.1145/3452917
Hague MMurawski AOng CSerre O(2017)Collapsible Pushdown Automata and Recursion SchemesACM Transactions on Computational Logic10.1145/309112218:3(1-42)Online publication date: 11-Aug-2017
https://dl.acm.org/doi/10.1145/3091122
Hague MKochems JOng C(2016)Unboundedness and downward closures of higher-order pushdown automataACM SIGPLAN Notices10.1145/2914770.283762751:1(151-163)Online publication date: 11-Jan-2016
https://dl.acm.org/doi/10.1145/2914770.2837627
Hague MKochems JOng CBodik RMajumdar R(2016)Unboundedness and downward closures of higher-order pushdown automataProceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages10.1145/2837614.2837627(151-163)Online publication date: 11-Jan-2016
https://dl.acm.org/doi/10.1145/2837614.2837627
Salvati SWalukiewicz I(2014)Krivine machines and higher-order schemesInformation and Computation10.1016/j.ic.2014.07.012239:C(340-355)Online publication date: 1-Dec-2014
https://dl.acm.org/doi/10.1016/j.ic.2014.07.012
Broadbent CCarayol AHague MSerre O(2013)C-SHOReACM SIGPLAN Notices10.1145/2544174.250058948:9(13-24)Online publication date: 25-Sep-2013
https://dl.acm.org/doi/10.1145/2544174.2500589
Broadbent CCarayol AHague MSerre OMorrisett GUustalu T(2013)C-SHOReProceedings of the 18th ACM SIGPLAN international conference on Functional programming10.1145/2500365.2500589(13-24)Online publication date: 25-Sep-2013
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Kobayashi N(2013)Model Checking Higher-Order ProgramsJournal of the ACM10.1145/2487241.248724660:3(1-62)Online publication date: 1-Jun-2013
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Carayol ASerre O(2012)Collapsible Pushdown Automata and Labeled Recursion SchemesProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.73(165-174)Online publication date: 25-Jun-2012
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