Abstract
We present the first implementation of Newton’s method for solving systems of equations over ω-continuous semirings (based on [5,11]). For instance, such equation systems arise naturally in the analysis of interprocedural programs or the provenance computation for Datalog. Our implementation provides an attractive alternative for computing their exact least solution in some cases where the ascending chain condition is not met and hence, standard fixed-point iteration needs to be combined with some over-approximation (e.g., widening techniques) to terminate. We present a generic C++ library along with the main algorithms and analyze their complexity. Furthermore, we describe our implementation of the counting semiring based on semilinear sets. Finally, we discuss motivating examples as well as performance benchmarks.
This work was partially funded by the DFG project “Polynomial Systems on Semirings: Foundations, Algorithms, Applications” and MT-LAB ( http://www.mt- lab.dk/ ).
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Schlund, M., Terepeta, M., Luttenberger, M. (2013). Putting Newton into Practice: A Solver for Polynomial Equations over Semirings. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2013. Lecture Notes in Computer Science, vol 8312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45221-5_48
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DOI: https://doi.org/10.1007/978-3-642-45221-5_48
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