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

Florent Jacquemard 1, 2 Luc Segoufin 3 Jérémie Dimino 4 
1 Repmus - Représentations musicales
STMS - Sciences et Technologies de la Musique et du Son
2 MuTant - Synchronous Realtime Processing and Programming of Music Signals
IRCAM - Institut de Recherche et Coordination Acoustique/Musique, UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
3 DAHU - Verification in databases
LSV - Laboratoire Spécification et Vérification [Cachan], Inria Saclay - Ile de France
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 FO 2 (<, +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 FO 2 (<, +1, ∼) but such that emptiness of DTA # and satisfiability of FO 2 (<, +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 FO 2 (<, +1, ∼) and emptiness of DTA # are equivalent.
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Submitted on : Friday, February 26, 2016 - 11:40:23 AM
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Florent Jacquemard, Luc Segoufin, Jérémie Dimino. FO2(<,+1,~) on data trees, data tree automata and branching vector addition systems.. Logical Methods in Computer Science, 2016, 12 (2), pp.32. ⟨10.2168/LMCS-12(2:3)2016⟩. ⟨hal-00769249v3⟩



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