  Using ideas from automata theory we design a new efficient (deterministic)
identity test for the \emph{noncommutative} polynomial identity testing problem
(first introduced and studied in \cite{RS05,BW05}). We also apply this idea to
the reconstruction of black-box noncommuting algebraic branching programs.
Assuming the black-box model allows us to query the ABP for the output at any
given gate, we can reconstruct an (equivalent) ABP in deterministic polynomial
time. Finally, we explore commutative identity testing when the coefficients of
the input polynomial come from an arbitrary finite commutative ring with unity.
