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Rapport (Rapport De Recherche) Année : 2015

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

Résumé

A data tree is a unranked ordered tree where each position 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 {DA#}, that is more expressive than {FO2(<,+1,~)} but such that emptiness of {DA#} 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 {DA#} are equivalent.
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Dates et versions

hal-00769249 , version 1 (30-12-2012)
hal-00769249 , version 2 (05-01-2015)
hal-00769249 , version 3 (26-02-2016)

Identifiants

  • HAL Id : hal-00769249 , version 1

Citer

Florent Jacquemard, Luc Segoufin, Jérémie Dimino. {FO2(<,+1, ~)} on data trees, data tree automata and an branching vector addition systems.. [Research Report] INRIA Saclay. 2015, pp.32. ⟨hal-00769249v1⟩
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