Mikołaj Bojańczyk, Tomasz Idziaszek
Algebra for Infinite Forests with an Application to the Temporal Logic EF. CONCUR, 2009 PDF
Mikołaj Bojańczyk, Thomas Place
Regular Languages of Infinite Trees That Are Boolean Combinations of Open Sets. ICALP (2), 2012 PDF
Mikołaj Bojańczyk, Tomasz Idziaszek, Michal Skrzypczak
Regular languages of thin trees. STACS, 2013 PDF
There are algebras for finite words (monoids or semigroups), infinite words (e.g. ω-semigroups or Wilke semigroups) and finite trees (e.g. clones or forest algebras). What about infinite trees? In  we propose a notion of algebra for infinite trees, which is an extension of forest algebra. It is not completely satisfactory (there is no result that finite algebras can be represented in a finite way), but it is good enough to characterize some logics, e.g. the temporal logic EF. The paper  continues the study of algebras for infinite trees, by giving a structural characterization of some random logic (namely, Boolean combinations of sets that are open in the Borel topology). The idea is to learn what kind of structural theory of regular tree languages is needed to do nontrivial characterizations. Finally, the last paper  shows that most of the technical problems go away when considering thin trees, which are infinite trees with countably many branches.