Function g is said to be a weak inversion of function f provided that g y = x if f x = y. A weak inversion exists for any function. In this
talk, we show that weak inversions can be derived automatically for a wide class of functions. As a nontrivial application, we demonstrate that weak inversion can be very useful for automatic parallelization of sequential programs, based on the well-known Third Homomorphism Theorem.

This is a joint work with Kazutaka Morita, Akimasa Morihata, Kimonori Matsuzaki, and Masato Takeichi.