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Global Value Numbering(GVN) is a popular method for detecting redundantcomputations. A polynomial time algorithm for GVN is presented by Gulwani andNecula(2006). Here we present two limitations of this GVN algorithm due towhich detection of certain kinds of redundancies can not be done using thisalgorithm. The first one is concerning the use of this algorithm in detectingsome instances of the classical global common subexpressions, and the second isconcerning its use in the detection of some redundancies that a local valuenumbering algorithm will detect. We suggest improvements that enable thealgorithm to detect these kinds of redundancies as well.

A Note on "A polynomial-time algorithm for global value numbering"