Abstract
Fixed point equations \({\bf\it X} = {\bf\it f}({\bf\it X})\) over ω-continuous semirings are a natural mathematical foundation of interprocedural program analysis. Generic algorithms for solving these equations are based on Kleene’s theorem, which states that the sequence \({\bf{0}}, {\bf\it f}({\bf{0}}), {\bf\it f}({\bf\it f}({\bf{0}})), \ldots\) converges to the least fixed point. However, this approach is often inefficient. We report on recent work in which we extend Newton’s method, the well-known technique from numerical mathematics, to arbitrary ω-continuous semirings, and analyze its convergence speed in the real semiring.
This work was in part supported by the DFG project Algorithms for Software Model Checking.
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Esparza, J., Kiefer, S., Luttenberger, M. (2008). Newton’s Method for ω-Continuous Semirings. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70583-3_2
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