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On the Expressive Power of Monadic Least Fixed Point Logic

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Automata, Languages and Programming (ICALP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3142))

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Abstract

Monadic least fixed point logic MLFP is a natural logic whose expressiveness lies between that of first-order logic FO and monadic second-order logic MSO. In this paper we take a closer look at the expressive power of MLFP. Our results are

  1. 1

    MLFP can describe graph properties beyond any fixed level of the monadic second-order quantifier alternation hierarchy.

  2. 2

    On strings with built-in addition, MLFP can describe at least all languages that belong to the linear time complexity class DLIN.

  3. 3

    Settling the question whether addition-invariant MLFP \(\stackrel{\mbox{\scriptsize ?}}{=}\) addition-invariant MSO on finite strings would solve open problems in complexity theory: “=” would imply that PH = PTIME, whereas “≠” would imply that DLIN ≠ LINH.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität Berlin, Unter den Linden 6, D-10099, Berlin, Germany

    Nicole Schweikardt

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  1. Nicole Schweikardt
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Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega, 240 Jordi Girona Salgado, 1-3 E-08034, Barcelona

    Josep Díaz

  2. Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. Department of Mathematics, University of Turku, Turku, Finland

    Arto Lepistö

  4. Laboratory for Foundations of Computer Science, University of Edinburgh,  

    Donald Sannella

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Schweikardt, N. (2004). On the Expressive Power of Monadic Least Fixed Point Logic. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_93

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  • DOI: https://doi.org/10.1007/978-3-540-27836-8_93

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22849-3

  • Online ISBN: 978-3-540-27836-8

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