Sequential Circuit Output Probabilities From Regular Expressions
- 1 March 1978
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Computers
- Vol. C-27 (3) , 222-231
- https://doi.org/10.1109/tc.1978.1675075
Abstract
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.Keywords
This publication has 9 references indexed in Scilit:
- The Error Latency of a Fault in a Sequential Digital CircuitIEEE Transactions on Computers, 1976
- Probabilistic Treatment of General Combinational NetworksIEEE Transactions on Computers, 1975
- The Probability of a Correct Output from a Combinational CircuitIEEE Transactions on Computers, 1975
- Analysis of Logic Circuits with Faults Using Input Signal ProbabilitiesIEEE Transactions on Computers, 1975
- Regular Expressions from Sequential CircuitsIEEE Transactions on Electronic Computers, 1964
- Derivatives of Regular ExpressionsJournal of the ACM, 1964
- Signal Flow Graph Techniques for Sequential Circuit State DiagramsIEEE Transactions on Electronic Computers, 1963
- A Survey of Regular Expressions and Their ApplicationsIRE Transactions on Electronic Computers, 1962
- Regular Expressions and State Graphs for AutomataIEEE Transactions on Electronic Computers, 1960