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Unsafe Grammars and Panic Automata

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Automata, Languages and Programming (ICALP 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3580))

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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 pop 1 and pop 2 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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Author information

Authors and Affiliations

  1. Université de la Nouvelle Calédonie,  

    Teodor Knapik

  2. Institute of Informatics, Warsaw University,  

    Damian Niwiński & Paweł Urzyczyn

  3. CNRS LaBRI, Université Bordeaux-1,  

    Igor Walukiewicz

Authors
  1. Teodor Knapik
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  2. Damian Niwiński
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  3. Paweł Urzyczyn
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  4. Igor Walukiewicz
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Editor information

Editors and Affiliations

  1. CITI / Departamento de Informática, Universidade Nova de Lisboa, Portugal

    Luís Caires

  2. Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Roma, Italy

    Giuseppe F. Italiano

  3. Departamento de Informatica, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Luís Monteiro

  4. Ecole Polytechnique, Rue de Saclay, 91128, Palaiseau Cedex, France

    Catuscia Palamidessi

  5. Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, NY 10027, New York, USA

    Moti Yung

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© 2005 Springer-Verlag Berlin Heidelberg

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Knapik, T., Niwiński, D., Urzyczyn, P., Walukiewicz, I. (2005). Unsafe Grammars and Panic Automata. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_117

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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27580-0

  • Online ISBN: 978-3-540-31691-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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