=ADD=
=reftype=
14
=number=
00-23
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2000/00-23.ps.gz
=year=
2000
=month=
06
=author=
Ratschan; Stefan
=title=
Convergence of Approximate Constraint Solving by Approximate Quantifiers
=abstract=
In this paper we are interested in solving quantified real constraints (i.e.,
first-order formulas over the real numbers). When trying to solve such
constraints exactly, one faces the following problems: First, constants
coming from measurements are often only approximately given. Second, solving
such constraints is in general undecidable and for special cases highly
complex. Third, exact solutions are often extremely complicated symbolic
expressions.

Thus we do approximate computation instead --- working on approximate inputs and
producing approximate output. One of the oldest approaches for dealing with such
uncertainty is set theory. It has been used for this purpose from its beginnings in
laying the foundations of mathematics, to many modern practical applications, for
example in the area of interval mathematics. We show that set theory can be applied in a
similar way to solving quantified constraint approximately. For this we use the notion
of heterogenous power algebra, which results in a general framework for approximate
computation that can be applied in various different domains.
=sponsor=
FWF SFB1303