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 -