A hierarchy of PYPs can be formed by making the base distribution of a PYP another PYP, following a semantics whereby whenever a customer sits at an empty table in a restaurant, a new customer is also said to enter the restaurant for its base distribution.
each table at one level is equivalent to a customer at the next deeper level, creating the invariants: where u = t l−1 indicates the unigram backoff context of h. The recursion terminates at the lowest level where the base distribution is static.