TY - GEN

T1 - Recent results on polynomial identity testing

AU - Shpilka, Amir

PY - 2011

Y1 - 2011

N2 - Polynomial Identity Testing (PIT) is a fundamental problem in algebraic complexity: We are given a circuit computing a multivariate polynomial, over some field F, and we have to determine whether it is identically zero or not. Note that we want the polynomial to be identically zero and not just to be equal to the zero function so, for example, x2-x is the zero function over F2 but not the zero polynomial. The importance of this problem follows from its many applications: Algorithms for primality testing [2, 3], for deciding if a graph contains a perfect matching [19, 20, 8] and more, are based on reductions to the PIT problem (see the introduction of [18] for more applications).

AB - Polynomial Identity Testing (PIT) is a fundamental problem in algebraic complexity: We are given a circuit computing a multivariate polynomial, over some field F, and we have to determine whether it is identically zero or not. Note that we want the polynomial to be identically zero and not just to be equal to the zero function so, for example, x2-x is the zero function over F2 but not the zero polynomial. The importance of this problem follows from its many applications: Algorithms for primality testing [2, 3], for deciding if a graph contains a perfect matching [19, 20, 8] and more, are based on reductions to the PIT problem (see the introduction of [18] for more applications).

UR - http://www.scopus.com/inward/record.url?scp=79959324407&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-20712-9_31

DO - 10.1007/978-3-642-20712-9_31

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AN - SCOPUS:79959324407

SN - 9783642207112

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 397

EP - 400

BT - Computer Science - Theory and Applications - 6th International Computer Science Symposium in Russia, CSR 2011, Proceedings

Y2 - 14 June 2011 through 18 June 2011

ER -