New results on Noncommutative and Commutative Polynomial Identity Testing

Details New results on Noncommutative and Commutative Polynomial Identity Testing New results on Noncommutative and Commutative Polynomial Identity Testing

2008-01-03

arxiv.org/abs/0801.0514v1

Computer Science

Computational Complexity

23 pages, no figure

Scientific paper

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.

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