Enumeration of monadic second-order queries on trees

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We consider the enumeration problem of Monadic Second-Order (MSO) queries with first-order free variables over trees. In Bagan [2006] it was shown that this problem is in CONSTANT-DELAY lin . An enumeration problem belongs to CONSTANT-DELAY lin if for an input structure of size n it can be solved by: —an O ( n ) precomputation phase building an index structure, —followed by a phase enumerating the answers with no repetition and a constant delay between two consecutive outputs. In this article we give a different proof of this result based on the deterministic factorization forest decomposition theorem of Colcombet [2007].