Deterministic simulation of probabilistic constant depth circuits

Miklos Ajtai, Avi Wigderson
1985 26th Annual Symposium on Foundations of Computer Science (sfcs 1985)  
We explicitly construct, for every integer $n$ and $\varepsilon >0$, a family of functions (pseudo-random bit generators) $f_{n,\varepsilon}:{0,1}^{n^{\varepsilon}} \rightarrow {0,1}^n$ with the following property: for a random seed, the pseudorandom output "looks random" to any polynomial size, constant depth, unbounded fan-in circuit. Moreover, the functions $f_{n,\varepsilon}$ themselves can be computed by uniform polynomial size, constant depth circuits. Some (interrelated) consequences of this result are given below.
doi:10.1109/sfcs.1985.19 dblp:conf/focs/AjtaiW85 fatcat:5qb2lcvhabhznmf7msgi262rga