Summary
We consider a generalization of Kildall's lattice theoretic approach to data flow analysis, which we call monotone data flow analysis frameworks. Many flow analysis problems which appear in practice meet the monotonicity condition but not Kildall's condition called distributivity. We show that the maximal fixed point solution exists for every instance of every monotone framework, and that it can be obtained by Kildall's algorithm. However, whenever the framework is monotone but not distributive, there are instances in which the desired solution—the “meet over all paths solution” — differs from the maximal fixed point. Finally, we show the nonexistence of an algorithm to compute the meet over all paths solution for monotone frameworks.
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Work supported by NSF grant GJ-1052.
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Kam, J.B., Ullman, J.D. Monotone data flow analysis frameworks. Acta Informatica 7, 305–317 (1977). https://doi.org/10.1007/BF00290339
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DOI: https://doi.org/10.1007/BF00290339