Relating Paths in Transition Systems: The Fall of the Modal Mu-Calculus

  • Cătălin Dima
  • Bastien Maubert
  • Sophie PinchinatEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9234)


We revisit Janin and Walukiewicz’s classic result on the expressive completeness of the modal mu-calculus w.r.t. MSO, when transition systems are equipped with a binary relation over paths. We obtain two natural extensions of MSO and the mu-calculus: MSOwith path relation and the jumping mu-calculus. While “bounded-memory” binary relations bring about no extra expressivity to either of the two logics, “unbounded-memory” binary relations make the bisimulation-invariant fragment of MSO with path relation more expressive than the jumping mu-calculus: the existence of winning strategies in games with imperfect-information inhabits the gap.


Transition System Binary Relation Imperfect Information Winning Strategy Atomic Proposition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Cătălin Dima
    • 1
  • Bastien Maubert
    • 2
  • Sophie Pinchinat
    • 3
    Email author
  1. 1.Université Paris Est, LACLCréteilFrance
  2. 2.LORIA - CNRS / Université de LorraineNancyFrance
  3. 3.IRISAUniversité de Rennes 1RennesFrance

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