We present a new method for solving the fixed point equations that appear in the static analysis of programs by abstract interpretation. We introduce and analyze a policy iteration algorithm for monotone self-maps of complete lattices. We apply this algorithm to the particular case of lattices arising in the interval abstraction of values of variables. We demonstrate the improvements in terms of speed and precision over existing techniques based on Kleene iteration, including traditional wideningarrowing acceleration mecanisms.
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