Derivatives of Regular Expressions
Journal of the ACM (JACM)
The Probability of a Correct Output from a Combinational Circuit
IEEE Transactions on Computers
Analysis of Logic Circuits with Faults Using Input Signal Probabilities
IEEE Transactions on Computers
Probabilistic Treatment of General Combinational Networks
IEEE Transactions on Computers
The Error Latency of a Fault in a Sequential Digital Circuit
IEEE Transactions on Computers
Deriving Signal Constraints to Accelerate Sequential Test Generation
VLSID '97 Proceedings of the Tenth International Conference on VLSI Design: VLSI in Multimedia Applications
Minimal Detecting Transition Sequences: Application to Random Testing
IEEE Transactions on Computers
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This paper presents a number of methods for finding sequential circuit output probabilities using regular expressions. Various classes of regular expressions, based on their form, are defined and it is shown how to easily find multistep transition probabilities directly from the regular expressions. A new procedure for finding steady-state probabilities is given which proceeds either from a regular expression or a state diagram description. This procedure is based on the concept of synchronization of the related machine, and is useful for those problems where synchronization sequences exist. In the cases where these techniques can be utilized, substantial savings in computation can be realized. Furthermore, application to other areas such as multinomial Markov processes is immediate.