On the Borel complexity of MSO definable sets of branches

Mikołaj Bojańczyk*, Damian Niwiński, Alexander Rabinovich, Adam Radziwończyk-Syta, Michał Skrzypczak

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An infinite binaryword can be identified with a branch in the full binary tree. We consider sets of branches definable in monadic second-order logic over the tree, where we allow some extra monadic predicates on the nodes. We show that this class equals to the Boolean combinations of sets in the Borel class Σ02 over the Cantor discontinuum. Note that the last coincides with the Borel complexity of ω-regular languages.

Original languageEnglish
Pages (from-to)337-349
Number of pages13
JournalFundamenta Informaticae
Issue number4
StatePublished - 2010


  • Automata
  • Borel hierarchy
  • Infinite words
  • Monadic 2nd-order logic
  • Trees


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