Modeling dynamical systems, both for control purposes and to make predictions\nabout their behavior, is ubiquitous in science and engineering. Predictive\nstate representations (PSRs) are a recently introduced class of models for\ndiscrete-time dynamical systems. The key idea behind PSRs and the closely\nrelated OOMs (Jaeger's observable operator models) is to represent the state of\nthe system as a set of predictions of observable outcomes of experiments one\ncan do in the system. This makes PSRs rather different from history-based\nmodels such as nth-order Markov models and hidden-state-based models such as\nHMMs and POMDPs. We introduce an interesting construct, the systemdynamics\nmatrix, and show how PSRs can be derived simply from it. We also use this\nconstruct to show formally that PSRs are more general than both nth-order\nMarkov models and HMMs/POMDPs. Finally, we discuss the main difference between\nPSRs and OOMs and conclude with directions for future work.\n