A Polynomial-Time Algorithm for Global Value Numbering

We describe a polynomial-time algorithm for global value numbering, which is the problem of discovering equivalences among program sub-expressions. We treat all conditionals as non-deterministic and all program operators as uninterpreted. We show that there are programs for which the set of all equivalences contains terms whose value graph representation requires exponential size. Our algorithm discovers all equivalences among terms of size at most $s$ in time that grows linearly with $s$. For global value numbering, it suffices to choose $s$ to be the size of the program. Earlier deterministic algorithms for the same problem are either incomplete or take exponential time.