TY - JOUR
T1 - On the Borel complexity of MSO definable sets of branches
AU - Bojańczyk, Mikołaj
AU - Niwiński, Damian
AU - Rabinovich, Alexander
AU - Radziwończyk-Syta, Adam
AU - Skrzypczak, Michał
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
KW - Automata
KW - Borel hierarchy
KW - Infinite words
KW - Monadic 2nd-order logic
KW - Trees
UR - http://www.scopus.com/inward/record.url?scp=77949601925&partnerID=8YFLogxK
U2 - 10.3233/FI-2010-231
DO - 10.3233/FI-2010-231
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AN - SCOPUS:77949601925
VL - 98
SP - 337
EP - 349
JO - Fundamenta Informaticae
JF - Fundamenta Informaticae
SN - 0169-2968
IS - 4
ER -