Jacquemard, Florent and Segoufin, Luc and Dimino, Jerémie - FO2(<,+1,~) on data trees, data tree automata and branching vector addition systems

lmcs:1635 - Logical Methods in Computer Science, April 26, 2016, Volume 12, Issue 2
FO2(<,+1,~) on data trees, data tree automata and branching vector addition systems

Authors: Jacquemard, Florent and Segoufin, Luc and Dimino, Jerémie

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 DAD# that is more expressive than FO2(<,+1,~) but such that emptiness of DAD# 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 DAD# are equivalent.


Source : oai:arXiv.org:1601.01579
DOI : 10.2168/LMCS-12(2:3)2016
Volume: Volume 12, Issue 2
Published on: April 26, 2016
Submitted on: January 5, 2015
Keywords: Computer Science - Formal Languages and Automata Theory


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