Algebraic independence and blackbox identity testing
نویسندگان
چکیده
منابع مشابه
Algebraic Independence and Blackbox Identity Testing
Algebraic independence is a fundamental notion in commutative algebra that generalizes independence of linear polynomials. Polynomials {f1, . . . , fm} ⊂ K[x1, . . . , xn] (over a field K) are called algebraically independent if there is no non-zero polynomial F such that F (f1, . . . , fm) = 0. The transcendence degree, trdeg{f1, . . . , fm}, is the maximal number r of algebraically independen...
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Given access to independent samples of a distribution A over [n℄ [m℄, we show how to test whether the distributions formed by projecting A to each coordinate are independent, i.e., whether A is -close in the L1 norm to the product distribution A1 A2 for some distributionsA1 over [n℄ and A2 over [m℄. The sample complexity of our test is ~ O(n2=3m1=3poly( 1)), assuming without loss of generality ...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2013
ISSN: 0890-5401
DOI: 10.1016/j.ic.2012.10.004