  We briefly review the inside-outside and EM algorithm for probabilistic
context-free grammars. As a result, we formally prove that inside-outside
estimation is a dynamic-programming variant of EM. This is interesting in its
own right, but even more when considered in a theoretical context since the
well-known convergence behavior of inside-outside estimation has been confirmed
by many experiments but apparently has never been formally proved. However,
being a version of EM, inside-outside estimation also inherits the good
convergence behavior of EM. Therefore, the as yet imperfect line of
argumentation can be transformed into a coherent proof.
