Smooth dynamical systems which realize arithmetical and logical operations
Three decades of mathematical system theory
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
What's decidable about hybrid automata?
Journal of Computer and System Sciences
Towards formal verification of analog designs
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
PHAVer: algorithmic verification of hybrid systems past hytech
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design
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As VLSI fabrication technology progresses to 65nm feature sizes and smaller, transistors no longer operate as ideal switches. This motivates the verification of digital circuits using continuous models. Recently, we showed how such verification can be performed using projection based methods. However, the verification was slow, requiring nearly four CPU days to verify a nine-transistor toggle flip-flop. Here, we describe improvements to the reachability algorithms and optimizations of the software architecture. These produce a 15× reduction in computation time and significant reductions in the overapproximation errors. With these changes, the same toggle flip-flop can be verified in a few hours, making formal verification a viable alternative to circuit simulation.