Mathematical systems theory

, Volume 21, Issue 1, pp 187–221 | Cite as

The monadic second-order logic of graphs, II: Infinite graphs of bounded width

  • Bruno Courcelle


A countable graph can be considered as the value of a certain infinite expression, represented itself by an infinite tree. We establish that the set of finite or infinite (expression) trees constructed with a finite number of operators, the value of which is a graph satisfying a property expressed in monadic second-order logic, is itself definable in monadic second-order logic. From Rabin's theorem, the emptiness of this set of (expression) trees is decidable. It follows that the monadic second-order theory of an equational graph, or of the set of countable graphs of width less than an integerm, is decidable.


Regular System Program Scheme Finite Graph Quotient Graph Infinite Graph 
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Copyright information

© Springer-Verlag New York Inc 1988

Authors and Affiliations

  • Bruno Courcelle
    • 1
  1. 1.Laboratoire d'InformatiqueUniversité Bordeaux ITalenceFrance

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