  A natural and often used strategy when testing software is to use input
values at boundaries, i.e. where behavior is expected to change the most, an
approach often called boundary value testing or analysis (BVA). Even though
this has been a key testing idea for long it has been hard to clearly define
and formalize. Consequently, it has also been hard to automate.
  In this research note we propose one such formalization of BVA by, in a
similar way as to how the derivative of a function is defined in mathematics,
considering (software) program derivatives. Critical to our definition is the
notion of distance between inputs and outputs which we can formalize and then
quantify based on ideas from Information theory.
  However, for our (black-box) approach to be practical one must search for
test inputs with specific properties. Coupling it with search-based software
engineering is thus required and we discuss how program derivatives can be used
as and within fitness functions.
  This brief note does not allow a deeper, empirical investigation but we use a
simple illustrative example throughout to introduce the main ideas. By
combining program derivatives with search, we thus propose a practical as well
as theoretically interesting technique for automated boundary value (analysis
and) testing.
