FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
ASIAN'05 Proceedings of the 10th Asian Computing Science conference on Advances in computer science: data management on the web
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Among their many uses, growth processes (probabilistic amplification), were used for constructing reliable networks from unreliable components, and deriving complexity bounds of various classes of functions. Hence, determining the initial conditions for such processes is an important and challenging problem. In this paper we characterize growth processes by their initial conditions and derive conditions under which results such as Valiant''s (Valiant, 1984) hold. First, we completely characterize growth processes that use linear connectives. Second, by extending Savick\''y''s (Savick\''y, 1990) analysis, via ``Restriction Lemmas'''', we characterize growth processes that use monotone connectives, and show that our technique is applicable to growth processes that use other connectives as well.