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SUMMARY:Global Realisations of Local Specifications - Martin Otto\, Techni
 sche Universität Darmstadt\, Germany
DTSTART:20151106T140000Z
DTEND:20151106T150000Z
UID:TALK62250@talks.cam.ac.uk
CONTACT:Ohad Kammar
DESCRIPTION:The following situation is typical of several tasks of model\n
 construction that arise\, e.g.\, in connection with finite model\nproperti
 es and finite controllability: Given a finite set of local\ntemplates\, to
 gether with specifications of required and permitted\npairwise overlaps be
 tween them\, the task is to find finite global\nrealisations.\n\nWe approa
 ch this finite realisation task via a generic construction of\nreduced pro
 ducts with suitable groupoids. Due to strong acyclicity\nproperties\, thes
 e groupoids can serve as structural backbones in the\nconstruction of fini
 te realisations\, similar to the use of free groups\nin standard construct
 ions of infinite realisations. The construction\nis sufficiently generic a
 s to be compatible with symmetries of the\nspecification while also allowi
 ng us to avoid incidental cycles of\noverlaps up to any specified finite l
 ength. The resulting finite\nrealisations can be forced\n\n-- to realise s
 ymmetries built into the specification\, and\n-- to admit local homomorphi
 sms into any (finite or infinite)\n\nrealisation and in particular into th
 e canonical free realisation.  As\none consequence we obtain a new proof o
 f the finite-model-assertion in\na theorem of Herwig and Lascar\, which al
 lows us to lift local\nsymmetries of finite structures to global symmetrie
 s within classes\ndefined by forbidden homomorphisms. This in turn proves\
 , e.g.\, finite\ncontrollability for UCQ vs. guarded specifications.
LOCATION:FW26
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