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

abstract: A data tree is an unranked ordered tree where each node carries a label from a finite alphabet and a datum from some infinite domain. We consider the two variable first order logic FO2(<, +1, ∼) over data trees. Here +1 refers to the child and the next sibling relations while < refers to the descendant and following sibling relations. Moreover, ∼ is a binary predicate testing data equality. We exhibit an automata model, denoted DTA# , that is more expressive than FO2(<, +1, ∼) but such that emptiness of DTA# and satisfiability of FO2(<, +1, ∼) are inter-reducible. This is proved via a model of counter tree automata, denoted EBVASS, that extends Branching Vector Addition Systems with States (BVASS) with extra features for merging counters. We show that, as decision problems, reachability for EBVASS, satisfiability of FO2(<, +1, ∼) and emptiness of DTA# are equivalent.

Recommended citation: Florent Jacquemard, Luc Segoufin, Jérémie Dimino, "FO2(<,+1,~) on data trees, data tree automata and branching vector addition systems" Logical Methods in Computer Science 12(2), 2016.