On the Bisimulation Invariant Fragment of Monadic Σ1 in the Finite

  • Anuj Dawar
  • David Janin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3328)


We investigate the expressive power of existential monadic second-order logic (monadic Σ1) on finite transition systems. In particular, we look at its power to express properties that are invariant under forms of bisimulation and compare these to properties expressible in corresponding fixed-point modal calculi. We show that on finite unary transition systems the bisimulation invariant fragment of monadic Σ1 is equivalent to bisimulation-invariant monadic second order logic itself or, equivalently, the mu-calculus. These results contrast with the situation on infinite structures. Although we show that these results do not extend directly to the case of arbitrary finite transition systems, we are still able to show that the situation there contrasts sharply with the case of arbitrary structures. In particular, we establish a partial expressiveness result by means of tree-like tiling systems that does not hold on infinite structures.


Modal Logic Transition System Modal Depth Expressive Power Regular Language 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Anuj Dawar
    • 1
  • David Janin
    • 2
  1. 1.Computer LaboratoryUniversity of CambridgeCambridgeUK
  2. 2.LaBRIUniversité Bordeaux ITalenceFrance

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