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2016
ACM

Newtonian program analysis via tensor product

1 years 5 months ago
Newtonian program analysis via tensor product
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
Added 09 Apr 2016
Updated 09 Apr 2016
Type Journal
Year 2016
Where POPL
Authors Thomas W. Reps, Emma Turetsky, Prathmesh Prabhu
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