It is generally agreed that flows indicate nothing more than a redundancy in the description of the dynamics of a system,[citation needed] but often, it is simpler computationally to work with a redundant description.
The on-shell solutions are given by the variational problem of extremizing the action subject to boundary conditions.
Suppose we have a "flow", i.e. the generator of a smooth one-dimensional group of transformations of the configuration space, which maps on-shell states to on-shell states while preserving the boundary conditions.
Even though this is technically a flow, this would usually not be considered a gauge symmetry because it is not local.
Flows can be given as derivations over the algebra of smooth functionals over the configuration space.