Generalising Automaticity to Modal Properties of Finite Structures

  • A. Dawar
  • S. Kreutzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2556)


We introduce a complexity measure of modal properties of finite structures which generalises the automaticity of languages. It is based on graph-automata like devices called labelling systems. We define a measure of the size of a structure that we call rank, and show that any modal property of structures can be approximated up to any fixed rank n by a labelling system. The function that takes n to the size of the smallest labelling system doing this is called the labelling index of the property. We demonstrate that this is a useful and fine-grained measure of complexity and show that it is especially well suited to characterise the expressive power of modal fixed-point logics. From this we derive several separation results of modal and non-modal fixed-point logics, some of which are already known whereas others are new.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • A. Dawar
    • 1
  • S. Kreutzer
    • 2
  1. 1.University of Cambridge Computer LaboratoryCambridgeUK
  2. 2.LuFG Mathematische Grundlagen der InformatikRWTHAachen

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