Semirings and formal power series: their relevance to formal languages and automata
Handbook of formal languages, vol. 1
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Program analysis using weighted pushdown systems
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Weighted pushdown systems and trust-management systems
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Accelerated data-flow analysis
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Weighted dynamic pushdown networks
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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.