Quantitative Testing
Henrik Bohnenkamp, Marielle Stoelinga
We investigate the problem of specification based testing with dense
sets of inputs and outputs, in particular with imprecision as they
might occur due to imprecise measurements, numerical instability
or noisy channels. Using quantitative transition systems to describe
implementations and specifications, we introduce implementation relations
that capture a notion of correctness "up to epsilon", i.e. that allow
deviation of the implementations behavior from that of the specification
as long as it does not deviate more than epsilon. The deviations are
described as Hausdorff distances between certain sets of traces. The
implementation relations are conservative extensions of the well-known
ioco relation. We develop a testing algorithm that we show to be sound
and exhaustive with respect to the implementation relations introduced.