New results for random determination of equivalence of expressions
Gastón H. Gonnet · 1986
We devise several procedures based on signatures (or hashing functions) to determine equivalence of expressions in Random Polynomial Time (also called Probabilistic Polynomial Time) (RPT). We extend the previous results known to include various new functions that can be tested. These procedures return as result: “equivalent” or “not-equivalent”. The result “not-equivalent” is always correct, while the result “equivalent” is correct with probability at least 1 — ε. This probability depends on a random number generator and is independent of the problem being solved. In all our procedures, the value ε can be made arbitrarily small. This method works for determining equivalence over an important class of functions as well as answering other questions like linearity, polynomial dependence, squareness, independence, etc.