The Boolean functions computed by random Boolean formulas or how to grow the right function - Brodsky, Alex; Pippenger, Nicholas (Random structures & algorithms, 2005)
We characterize growth processes (probabilistic amplification) by their initial conditions to derive conditions under which results such as Valiant's J Algorithms 5 (1984), 363–366 hold. We completely characterize growth processes that use linear connectives and generalize Savický's Discrete Math 147 (1990), 95–103 analysis to characterize growth processes that use monotone connectives. Additionally, we obtain explicit bounds on the convergence rates of several growth processes, including the growth process studied in Savický. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005