I'm learning about OBDD and I have learned that the size of a reduced OBDD (ROBDD) is dependent on the ordering of the variables, and that finding an optimal ordering is an NP hard problem.
Say I already have one ROBDD by some ordering, I can, in some cases, determine if it optimal:for example if each variable appear only once (the optimality follows from the fact that a ROBDD does not contain variables that the formula doesn't depend on)
My question is this - Can I always tell if a ROBDD is optimal by some given relation ?
This would be true if a ROBDD must have each variable at most once (this is a claim I haven't managed to prove).
