Abstract
Polynomial Identity Testing (PIT) algorithms have focussed on polynomials computed either by small alternation-depth arithmetic circuits, or by read-restricted formulas. Read-once polynomials (ROPs) are computed by read-once formulas (ROFs) and are the simplest of read-restricted polynomials. Building structures above these, we show:
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1
A deterministic polynomial-time non-black-box PIT algorithm for ∑ (2)· ∏ ·ROF.
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2
Weak hardness of representation theorems for sums of powers of constant-free ROPs and for 0-justified alternation-depth-3 ROPs.
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Mahajan, M., Rao, B.V.R., Sreenivasaiah, K. (2014). Building above Read-once Polynomials: Identity Testing and Hardness of Representation. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_1
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DOI: https://doi.org/10.1007/978-3-319-08783-2_1
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