Probability Theory, Mathematical Statistics, and Theoretical Cybernetics

This work is a continuation of earlier volumes under the heading "Probability Theory, Mathematical Statistics, and Theo- retical Cybernetics," published as part of the "Itogi Nauki" series. The present volume comprises a single review article, en- titled "Reliability of Discrete Systems," covering material pub- lished mainly in the last six to eight years and abstracted in "Referativnyi Zhurnal-Matematika" (Soviet Abstract Journal in Mathematics). The bibliography encompasses 313 items. The editors welcome inquiries regarding the present volume or the format and content of future volumes of the series; corre- spondence should be sent to the following address: Otdel Matemat- ika (Mathematics Section), Baltiiskaya ul., 14, Moscow, A-219. v Contents RELIABILITY OF DISCRETE SYSTEMS M. A. Gavrilov, V. M. Ostianu, and A. I. Potekhin Introduction ...* ...* ...1 ...CHAPTER 1. Assurance of Infallibility in Discrete Systems...5 1. State of the Art .*...*...5 2. Basic Definitions, Concepts, and Problem Formulations. 6 3. Redundancy Models...*...10 . * . . 4. Composition Methods ...17 5. Majority Methods ...*...27 ...6. Methods Using the Interweaving Model...35 7. Methods Using Effective-Coding Models...38 CHAPTER II. Assurance of Stability in Discrete System s...63 ...1. Basic Concepts and Definitions ...63 . . 2. Elimination of Inadmissible I-Races...69 . 3. Elimination of Inadmissible E-Races ...70 . 4. Elimination of Inadmissible M-Races ...73 . 5. Elimination of Inadmissible L-Races ...86 .