The following technical report is available from
http://aib.informatik.rwth-aachen.de:
Lower Runtime Bounds for Integer Programs
Florian Frohn, Matthias Naaf, Jera Hensel, Marc Brockschmidt, and
Jürgen Giesl
AIB 2016-03
We present a technique to infer lower bounds on the worst-case
runtime complexity of integer programs. To this end, we construct
symbolic representations of program executions using a framework for
iterative, under-approximating program simplification. The core of
this simplification is a method for (under-approximating) program
acceleration based on recurrence solving and a variation of ranking
functions. Afterwards, we deduce asymptotic lower bounds from the
resulting simplified programs. We implemented our technique in our
tool LoAT and show that it infers non-trivial lower bounds for a
large number of examples.