Formal timing analysis of gate-level digital circuits using model checking

Due to the continuous reduction in the transistors sizing ruled by the Moore's law, digital devices have become smaller, and more complex resulting in an enormous rise in the delay variations. Therefore, there is a dire need of precise and rigorous timing analysis to overcome anomalies during the timing analysis. Timings of digital circuits can be verified using various simulation or static timing analysis (STA) based tools but they provide estimated results due to their inherent in-exhaustive nature or report timing paths corresponding to non-existent functional paths, respectively. Formal verification provides complete and sound analysis results and has widely been used for the functional verification of digital circuits but its application in the timing analysis domain is somewhat limited. We present a generic framework to perform formal timing analysis of digital circuits with the help of Uppaal model-checker. The given digital circuit along with its timing parameters in the form of state transition diagram are modeled using timed automata in the Uppaal model checker. Timing delays are calculated from corresponding technology parameters, and Quartus Prime Pro is used to obtain the information about the circuits' paths. In order to make the analysis scalable, we also propose a novel path partitioning technique and compare its results with complete path analysis and traditional STA. The formal model is verified with the help of properties to assess the timing characteristics, like time period of a clock, critical path, and propagation delay of the considered circuit. Modeling and verification of ISCAS-85 and ISCAS-89 benchmark circuits is presented for illustration purposes.