PSPACE Survives Three-Bit Bottlenecks

Barrington recently discovered that polynomial-size logarithmic-depth circuits are equivalent to constant-width branching programs [B]. We discuss the relationship between constant-width branching programs and a hierarchy of languages that lies between Ρ and PSPACE. We also introduce the notion of logspace-serializability. For relativized computations, this notion corresponds to logspace-uniform, constant-width branching programs. Applying Barrington's method we show that PSPACE is logspace-serializable.