  We study generalized fixed-point equations over idempotent semirings and
provide an efficient algorithm for the detection whether a sequence of Kleene's
iterations stabilizes after a finite number of steps. Previously known
approaches considered only bounded semirings where there are no infinite
descending chains. The main novelty of our work is that we deal with semirings
without the boundedness restriction. Our study is motivated by several
applications from interprocedural dataflow analysis. We demonstrate how the
reachability problem for weighted pushdown automata can be reduced to solving
equations in the framework mentioned above and we describe a few applications
to demonstrate its usability.
