Theory of Computing Systems

, Volume 48, Issue 1, pp 93–131 | Cite as

Fixpoint Logics over Hierarchical Structures



Hierarchical graph definitions allow a modular description of graphs using modules for the specification of repeated substructures. Beside this modularity, hierarchical graph definitions also allow to specify graphs of exponential size using polynomial size descriptions. In many cases, this succinctness increases the computational complexity of decision problems. In this paper, the model-checking problem for the modal μ-calculus and (monadic) least fixpoint logic on hierarchically defined input graphs is investigated. In order to analyze the modal μ-calculus, parity games on hierarchically defined input graphs are investigated. Precise upper and lower complexity bounds are derived. A restriction on hierarchical graph definitions that leads to more efficient model-checking algorithms is presented.


Parity games μ-calculus Hierarchical structures Model-checking Complexity 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Fachbereich 3Universität BremenBremenGermany
  2. 2.Institut für InformatikUniversität LeipzigLeipzigGermany

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