  The notion of reparametrizations of Weighted CSPs (WCSPs) (also known as
equivalence-preserving transformations of WCSPs) is well-known and finds its
use in many algorithms to approximate or bound the optimal WCSP value. In
contrast, the concept of super-reparametrizations (which are changes of the
weights that keep or increase the WCSP objective for every assignment) was
already proposed but never studied in detail. To fill this gap, we present a
number of theoretical properties of super-reparametrizations and compare them
to those of reparametrizations. Furthermore, we propose a framework for
computing upper bounds on the optimal value of the (maximization version of)
WCSP using super-reparametrizations. We show that it is in principle possible
to employ arbitrary (under some technical conditions) constraint propagation
rules to improve the bound. For arc consistency in particular, the method
reduces to the known Virtual AC (VAC) algorithm. We implemented the method for
singleton arc consistency (SAC) and compared it to other strong local
consistencies in WCSPs on a public benchmark. The results show that the bounds
obtained from SAC are superior for many instance groups.
