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ICALP

2010

Springer

2010

Springer

We say that a polynomial f(x1, . . . , xn) is indecomposable if it cannot be written as a product of two polynomials that are deﬁned over disjoint sets of variables. The polynomial decomposition problem is deﬁned to be the task of ﬁnding the indecomposable factors of a given polynomial. Note that for multilinear polynomials, factorization is the same as decomposition, as any two diﬀerent factors are variable disjoint. In this paper we show that the problem of derandomizing polynomial identity testing is essentially equivalent to the problem of derandomizing algorithms for polynomial decomposition. More accurately, we show that for any reasonable circuit class there is a deterministic polynomial time (black-box) algorithm for polynomial identity testing of that class if and only if there is a deterministic polynomial time (black-box) algorithm for factoring a polynomial, computed in the class, to its indecomposable components. An immediate corollary is that polynomial identity ...

Related Content

Added |
19 Jul 2010 |

Updated |
19 Jul 2010 |

Type |
Conference |

Year |
2010 |

Where |
ICALP |

Authors |
Amir Shpilka, Ilya Volkovich |

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