Constant Width Planar Branching Programs Characterize ACC^0 in Quasipolynomial Size

Abstract

We revisit the computational power of constant width polynomial size planar nondeterministic branching programs. We show that they are capable of computing any function computed by a Pi₂ o CC⁰ o AC⁰ circuit in polynomial size. In the quasipolynomial size setting we obtain a characterization of ACC⁰ by constant width planar non-deterministic branching programs.