Mathematical systems theory

, Volume 21, Issue 1, pp 187–221

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

• Bruno Courcelle
Article

## Abstract

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.

## Keywords

Regular System Program Scheme Finite Graph Quotient Graph Infinite Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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