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Self-similar structure of wire length distribution of random logic

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  • Matsuba, Ikuo

Abstract

A general scaling theory is proposed to estimate a wire length distribution based on the self-similarity structure of random logic. It is theoretically shown that the d-dimensional wire length distribution denoted by fℓ(d) is of the form fℓ(d)∼ℓ-γ1(d) with a characteristic exponent γ1(d)=α(d)+2−dp for ℓ<ℓcrossover with some crossover length ℓcrossover, where ℓ is a wire length and p is the Rent’s partition exponent. The parameter α(d) is equal to d−1 and d for serialized and parallel wiring configurations, respectively. For wire lengths larger than ℓcrossover, fℓ(d)∼ℓ-γ2(d) is obtained with γ2(d)=α(d)+2. These results are in good agreement with experiments.

Suggested Citation

  • Matsuba, Ikuo, 2007. "Self-similar structure of wire length distribution of random logic," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 85-94.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:85-94
    DOI: 10.1016/j.chaos.2005.09.043
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