  Iterated belief revision requires information about the current beliefs. This
information is represented by mathematical structures called doxastic states.
Most literature concentrates on how to revise a doxastic state and neglects
that it may exponentially grow. This problem is studied for the most common
ways of storing a doxastic state. All four methods are able to store every
doxastic state, but some do it in less space than others. In particular, the
explicit representation (an enumeration of the current beliefs) is the more
wasteful on space. The level representation (a sequence of propositional
formulae) and the natural representation (a history of natural revisions) are
more compact than it. The lexicographic representation (a history of
lexicographic revision) is even more compact than them.
