Implicit Resolution of the Chapman-Kolmogorov Equations for Sequential Circuits: An Application in Power Estimation
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- TL;DR
- This research introduces an implicit method for formulating and solving the Chapman-Kolmogorov equations to determine state probabilities in the stationary behavior of sequential circuits.
- Problem
- Previous approaches to power estimation assumed uncorrelated input signals, failing to capture the more general case of inputs driven by a discrete time Markov chain with temporal and spatial correlations.
- Method
- The approach models input sequences using a discrete time Markov chain described implicitly via a formalism that compactly represents exponentially large state spaces, enabling power estimation that accounts for both primary input and internal signal correlations.
- Results
- The method successfully demonstrates the exact solution of Chapman-Kolmogorov equations for systems comprising more than $10^7$ equations in certain cases.
- Contributions
- An implicit formulation and solution technique for Chapman-Kolmogorov equations applied to the power estimation of sequential circuits under correlated input conditions.
- Limitations
- Not specified in the abstract.
- Takeaways
- Implicitly solving Chapman-Kolmogorov equations makes it feasible to exactly analyze sequential circuit systems with over $10^7$ equations while fully accounting for signal correlations.
- Applications
- Power estimation for sequential circuits.
- Topics
- Implicit Resolution; Chapman-Kolmogorov Equations; Sequential Circuits; Power Estimation
- For industry
- Semiconductor design and electronic hardware development.
- Why it matters
- Improves the accuracy of power estimation in digital hardware by handling complex signal correlations in systems with massive state spaces.
Abstract
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 10 7 equations.