We investigate the computational complexity of the
isomorphism problem for one-time-only branching programs (BP1-Iso):
on input of two one-time-only branching programs B and B',
decide whether there exists a permutation of the variables of B'
such that it becomes equivalent to B.
Our main result is a two-round interactive proof for the complement of BP1-Iso.
The protocol is based on the Schwartz-Zippel Theorem
to probabilistically check polynomial idendities.
As a consequence,
BP1-Iso cannot be NP hard unless the polynomial hierarchy collapses.
We extend the protocol to get an interactive proof to decide the
non-isomorphism of multivariate polynomials over an arbitrary field.
Finally, we show that BP1-Iso has a zero-knowledge interactive proof.
