Equations for hidden Markov models

We will outline novel approaches to derive model invariants for hidden Markov and related models. These approaches are based on a theoretical framework that arises from viewing random processes as elements of the vector space of string functions. Theorems available from that framework then give rise to novel ideas to obtain model invariants for hidden Markov and related models.
Comment: 28 pages; Results presented at the Workshop on Algebraic Statistics, MSRI, UC Berkeley, Dec. 2008. Simplified arguments