Newtonian program analysis via tensor product

8 years 11 days ago

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Recently, Esparza et al. generalized Newton’s method—a numerical-analysis algorithm for ﬁnding roots of real-valued functions—to a method for ﬁnding ﬁxed-points of systems of equations over semirings. Their method provides a new way to solve interprocedural dataﬂow-analysis problems. As in its real-valued counterpart, each iteration of their method solves a simpler “linearized” problem. One of the reasons this advance is exciting is that some numerical analysts have claimed that “‘all’ effective and fast iterative [numerical] methods are forms (perhaps very disguised) of Newton’s method.” However, there is an important difference between the dataﬂow-analysis and numerical-analysis contexts: when Newton’s method is used on numerical-analysis problems, multiplicative commutativity is relied on to rearrange expressions of the form “c ∗ X + X ∗ d” into “(c + d) ∗ X.” Such equations correspond to path problems described by regular languages. In...

Thomas W. Reps, Emma Turetsky, Prathmesh Prabhu

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