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A data tree is an unranked ordered tree where each node carries a label froma finite alphabet and a datum from some infinite domain. We consider the twovariable first order logic FO2(<,+1,~) over data trees. Here +1 refers to thechild and the next sibling relations while < refers to the descendant andfollowing sibling relations. Moreover, ~ is a binary predicate testing dataequality. We exhibit an automata model, denoted DAD# that is more expressivethan FO2(<,+1,~) but such that emptiness of DAD# and satisfiability ofFO2(<,+1,~) are inter-reducible. This is proved via a model of counter treeautomata, denoted EBVASS, that extends Branching Vector Addition Systems withStates (BVASS) with extra features for merging counters. We show that, asdecision problems, reachability for EBVASS, satisfiability of FO2(<,+1,~) andemptiness of DAD# are equivalent.

FO2(<,+1,~) on data trees, data tree automata and branching vector addition systems