I am learning the methods for proving lower bounds on streaming algorithms using communication complexity.
My question is about a basic technique to prove lower bounds on streaming models using the reduction by giving each player in the communication game a fragment of the tape of Turing Machine whose sequential scan is bounded.The number of sequential scans is the number of passes.
We consider streaming algorithm as a one tape TM.
Is there some inherent limitations of this reduction using fragments of the tape?
It seems that increasing of the number of passes deteriorates the efficiency of reductions and that we would not use this fragment methods to prove lower bounds on streaming models with many passes.
Are there other powerful methods which overcome the weakness of the fragment methods?