Satisfiability of ECTL* with Tree Constraints

  • Claudia Carapelle
  • Shiguang Feng
  • Alexander Kartzow
  • Markus Lohrey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9139)


Recently, we proved that satisfiability for \(\mathsf {ECTL}^*\) with constraints over \(\mathbb {Z}\) is decidable using a new technique based on weak monadic second-order logic with the bounding quantifier (\(\mathsf {WMSO\!+\!B}\)). Here we apply this approach to concrete domains that are tree-like. We show that satisfiability of \(\mathsf {ECTL}^*\) with constraints is decidable over (i) semi-linear orders, (ii) ordinal trees (semi-linear orders where the branches form ordinals), and (iii) infinitely branching order trees of height h for each fixed \(h\in \mathbb {N}\). In contrast, we introduce Ehrenfeucht-Fraïssé-games for \(\mathsf {WMSO\!+\!B}\) (weak \(\mathsf {MSO}\) with the bounding quantifier) and use them to show that our approach cannot deal with the class of order trees. Missing proofs and details can be found in the long version [6].



We thank Manfred Droste for fruitful discussions on universal structures and semi-linear orders and the anonymous referees.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Claudia Carapelle
    • 1
  • Shiguang Feng
    • 1
  • Alexander Kartzow
    • 2
  • Markus Lohrey
    • 2
  1. 1.Institut für InformatikUniversität LeipzigLeipzigGermany
  2. 2.Department für Elektrotechnik Und InformatikUniversität SiegenSiegenGermany

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