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We study generalized fixed-point equations over idempotent semirings andprovide an efficient algorithm for the detection whether a sequence of Kleene'siterations stabilizes after a finite number of steps. Previously knownapproaches considered only bounded semirings where there are no infinitedescending chains. The main novelty of our work is that we deal with semiringswithout the boundedness restriction. Our study is motivated by severalapplications from interprocedural dataflow analysis. We demonstrate how thereachability problem for weighted pushdown automata can be reduced to solvingequations in the framework mentioned above and we describe a few applicationsto demonstrate its usability.

Interprocedural Dataflow Analysis over Weight Domains with Infinite Descending Chains