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Optimal design of linear consecutive systems

Published:03 October 2022Publication History

ABSTRACT

A critical issue for few nanometers technologies is the cost-yield balance, clearly tilted by soaring costs. An option to reduce costs, while also increasing yield, is to use reliability enhancement schemes. Unfortunately, these are considered power-hungry (due to redundancy), and entailing complex designs. From biology, neurons are prime examples of efficiency, achieving outstanding communication reliabilities, although relying on random ion channels. Aiming to bridge from biology to circuits, we will show how overlooked statistical results (about linear consecutive systems), combined with a Binet-like formula (for Fibonacci numbers of higher orders), allow avoiding lengthy reliability calculations, and present a straightforward neuron-inspired optimal design scheme for reliable communications.

References

  1. Valeriu Beiu et al. 2023. Bridging reliability to efficiency. In Proc. Intl. Conf. Comp. Comm. & Ctrl., Băile Felix, Romania, Springer, in press (2023).Google ScholarGoogle Scholar
  2. Edward F. Moore and Claude E. Shannon. 1956. Reliable circuits using less reliable relays - Part I. J. Franklin Inst. 262, 3 (1956), 191--208.Google ScholarGoogle ScholarCross RefCross Ref
  3. John M. Kontoleon. 1980. Reliability determination of a r-succesiveout-of-n:F system. IEEE Trans. Rel. R-29, 5 (1980), 437.Google ScholarGoogle ScholarCross RefCross Ref
  4. Dalen T. Chiang and Shun-Chen Niu. 1981. Reliability of consecutive-k-out-of-n:F system. IEEE Trans. Rel. R-30, 1 (1981), 87--89.Google ScholarGoogle ScholarCross RefCross Ref
  5. Abraham de Moivre. 1738. The Doctrine of Chances (2nd. ed.). H. Woodfall: London, UK. Available at 01LINDAHALL_INST:LHL/1287366660005961Google ScholarGoogle Scholar
  6. Leslie G. Valiant. 1979. The complexity of enumeration and reliability problems. SIAM J. Comp. 8, 3 (1979), 410--421.Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Valeriu Beiu and Leonard Dăuş. 2014. Deciphering the reliability scheme of the neurons. In Proc. Int. Conf. Bio-insp. ICT, Boston, MA, 182--187 (2014).Google ScholarGoogle Scholar
  8. Ke Xu et al. 2013. Actin, spectrin and associated proteins form a periodic cytoskeletal structure in axons. Science 339, 6118 (2013), 452--456.Google ScholarGoogle Scholar
  9. Valeriu Beiu and Leonard Dăuş. 2014. Reliability bounds for two dimensional consecutive systems. Nano Comm. Nets. 6, 3 (2015), 145--152.Google ScholarGoogle ScholarCross RefCross Ref
  10. Maurice d'Ocagne. 1883. Sur un algorithme algébrique. Nouv. Ann. Math. 2 (1883), 220--226. Available at id=NAM_1883_3_2__220_0Google ScholarGoogle Scholar
  11. David A. Wolfram. 1998. Solving generalized Fibonacci recurrences. Fibonacci Quart. 36, 2 (1998), 129--145.Google ScholarGoogle Scholar
  12. Gregory P. B. Dresden, Zhaohui Du. 2014. A simplified Binet formula for k-generalized Fibonacci numbers. J. Integer Seq. 17, 4 (2014), art. 14.4.7 (1--9).Google ScholarGoogle Scholar
  13. Harold D. Shane. 1973. A Fibonacci probability function. Fibonacci Quart. 11, 5 (1973), 517--522.Google ScholarGoogle Scholar
  14. Stephen J. Turner. 1979. Probability via the nth-order Fibonacci-T sequence. Fibonacci Quart. 17, 1 (1979), 23--28.Google ScholarGoogle Scholar
  15. Andreas N. Philippou et al. 1985. Fibonacci-type polynomials of order k with probability applications. Fibonacci Quart. 23, 2 (1985), 100--105.Google ScholarGoogle Scholar
  16. Frank K. Hwang and Shi Dinghua. 1987. Redundant consecutive-k systems. Oper. Res. Lett. 6, 6 (1987), 293--296.Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Valeriu Beiu et al. 2023/4. The trustworthy wings of the mysterious butterflies of the soul. Nature Comm. (2023/4), in progress.Google ScholarGoogle Scholar

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            cover image ACM Other conferences
            NANOCOM '22: Proceedings of the 9th ACM International Conference on Nanoscale Computing and Communication
            October 2022
            177 pages
            ISBN:9781450398671
            DOI:10.1145/3558583

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            Publication History

            • Published: 3 October 2022

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