Functional Characterizations of Uniform Log-depth and Polylog-depth Circuit Families

We characterize the classes of functions computable by uniform log-depth (NC1) and polylog-depth circuit families as closures of a set of base functions. (The former is equivalent to ALOGTIME, the latter to polylogarithmic space.) The closures involve the \safe" composition of Bellantoni and Cook as well as a safe \divide and conquer" recursion a simple change to the de nition of the latter distinguishes between log and polylog depth. The proofs proceed, in one direction, by showing that safe composition and divideand-conquer recursion preserve growth rate and circuit depth bounds, and in the other, by simulating alternating Turing machines with divide-and-conquer recursion.

• Type: Conference
• Year: 1992
• Where: COCO
• Authors: Stephen A. Bloch
• Keywords: Algorithms, Circuit Depth Bounds, COCO 1992, Polylog-depth Circuit Families, Recursion Preserve Growth