Implicit resolution of the Chapman-Kolmogorov equations for sequential circuits: an application in power estimation

In this work we describe an approach that implicitly formulates and solves the Chapman-Kolmogorov equations that describe the state probabilities associated with the stationary behavior of sequential circuits. Unlike previous approaches that assumed uncorrelated input signals, we model the more general case where the sequential circuit is driven by a sequence of inputs described by a discrete time Markov chain. This Markov chain is described implicitly using a formalism that allows for a compact description of chains with an exponentially high number of states. Using this approach, we present an application in power estimation of sequential circuits that takes into account all the temporal and spatial correlations between the primary inputs and the internal signals. We present results showing that, in some cases, it is possible to solve exactly the Chapman-Kolmogorov equations for systems with more than 10⁷ equations.