 
Summary: UIC Model Theory Seminar, April 12, 2005
A characterization of firstorder topological properties of planar
spatial databases
Michael Benedikt, Bell Laboratories
A spatial query is a firstorder sentence with predicates that range over semi
algebraic relations (or, more generally, definable relations in some ominimal
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
firstorder 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 ominimal 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.
