Boolean circuit is used to measure time in a nonuniform way, which Pippenger showed the relation between a time complexity of uniform model (Turing Machines) and size complexity of boolean circuits. In the theory of space complexity, branching programs are considered to measure nonuniform space complexity.
I want a survey to answer the following question. My motivation came from the state of the art of attempts for separation between NL and L, that is , proving L vs NL problem. I would like to know whether there is any analogous approach for proving separation between time complexity classes (deriving circuit lower bounds is useful for separation of time complexity classes because this approach is supported by Pippenger's theorem). Thus I would like to know whether there is an analogue of Pippernger's theorem which would support non-uniform approaches for separation of the space complexity classes like circuit lower bounds.
Is there a Nondeterministic polynomial size branching program solving an NL-complete problem if we take a Nondeterministic Turing Machine solving the same problem ?
N.Pippenger and M.Fischer, Relations among complexity measures, J of ACM, 1979.