Reference:

Morten Kühnrich, Stefan Schwoon, Jiří Srba, and Stefan Kiefer. Interprocedural dataflow analysis over weight domains with infinite descending chains. In Luca de Alfaro, editor, Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures (FOSSACS), volume 5504 of LNCS, pages 440–455, York, UK, March 2009. Springer.

Abstract:

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.

Suggested BibTeX entry:

@inproceedings{KSSK09c,
    address = {York, UK},
    author = {Morten K\"uhnrich and Stefan Schwoon and Ji\v{r}\'{\i} Srba and Stefan Kiefer},
    booktitle = {Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures (FOSSACS)},
    editor = {Luca de Alfaro},
    month = {March},
    pages = {440--455},
    publisher = {Springer},
    series = {LNCS},
    title = {Interprocedural Dataflow Analysis over Weight Domains with Infinite Descending Chains},
    volume = {5504},
    year = {2009}
}