Progress in Mathematics

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 .â¢.......â¢.................. 5 2. Basic Definitions, Concepts, and Problem Formulations.. 6 3. Redundancy Models. . . . . . . . . . . . . . . . . . â¢. . . 10 . ⢠. . 4. Composition Methods ........................ 17 5. Majority Methods . . . . . . . . . . . . . . . . . . . â¢. . . 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 .