Assurance of Infallibility in Discrete Systems

  • R. V. Gamkrelidze
Part of the Progress in Mathematics book series (PM, volume 13)


The earliest studies of reliability assurance by the introduction of redundancy were basically concerned with the notion of simple composition (replication). Composition methods are time-honored and merely entail the complementation of a particular component or module of a system with one or more redundant replicas of the component or module, which either take over the function of the primary object in the event of failure (passive, or “cold,” composition) or operate simultaneously with the primary object (active, or “hot” composition). Essentially, however, the modern theory of reliability assurance through the introduction of redundancy was developed and its fundamental disciplines defined at a later date. This theory had its genesis in von Neumann’s six lectures on probabilistic logic at the California Institute of Technology in 1952; the lectures were subsequently published in the now-classical treatise [269]. Somewhat later Moore and Shannon published their paper [263] on the synthesis of reliability circuits from unreliable relays. With the advent of information theory, particularly the branch thereof known as coding theory, the growing tendency was to regard discrete systems as special kinds of channels, namely computation channels, and to treat them with the reliability improvement techniques used in communication channels. The legitimacy of this approach was investigated by Elias [196], and the practical application of coding to discrete systems of a particular type was explored by Gavrilov [9] and Zakrevskii [35].


Boolean Function Failure Probability Discrete System Majority Organ Primary System 
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Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • R. V. Gamkrelidze
    • 1
  1. 1.V.A. Steklov Mathematics InstituteAcademy of Sciences of the USSRMoscowRussia

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