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UIC Model Theory Seminar, April 12, 2005 A characterization of first-order topological properties of planar
 

Summary: UIC Model Theory Seminar, April 12, 2005
A characterization of first-order topological properties of planar
spatial databases
Michael Benedikt, Bell Laboratories
A spatial query is a first-order sentence with predicates that range over semi-
algebraic relations (or, more generally, definable relations in some o-minimal
expansion of the real field). A query is topological if (informally) it depends
only on the shape of a region. Our work concerns characterizing which
first-order sentences are topological. One cannot decide whether a query is
topological, but one can hope to give effective syntactic criteria capturing
exactly the topological queries. Our main result is a language capturing
topological queries in the case where the relation symbol is restricted to
be a closed region in the plane. I'll overview the proof, which combines
some (simple, old) results about queries over o-minimal structures, along
with some (pretty simple, but new) automata theory. The main tool from
automata theory is a characterization of which regular languages are first-
order definable relative to a modulus class. This is joint work with Christoph
Loeding, Jan van den Bussche, and Thomas Wilke.

  

Source: Aschenbrenner, Matthias - Department of Mathematics, University of California at Los Angeles

 

Collections: Mathematics