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More on Noncommutative Polynomial Identity Testing
"... We continue the study of noncommutative polynomial identity testing initiated by Raz and Shpilka and present efficient algorithms for the following problems in the noncommutative model: Polynomial identity testing: The algorithm gets as an input an arithmetic circuit with the promise that the polyno ..."
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Cited by 10 (0 self)
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We continue the study of noncommutative polynomial identity testing initiated by Raz and Shpilka and present efficient algorithms for the following problems in the noncommutative model: Polynomial identity testing: The algorithm gets as an input an arithmetic circuit with the promise
Fast probabilistic algorithms for verification of polynomial identities
 J. ACM
, 1980
"... ABSTRACT The starthng success of the RabmStrassenSolovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous ..."
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Cited by 520 (1 self)
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wgorous search for probabdisuc algonthms In dlustratmn of this observaUon, vanous fast probabdlsttc algonthms, with probability of correctness guaranteed a prion, are presented for testing polynomial ldentmes and propemes of systems of polynomials. Ancdlary fast algorithms for calculating resultants
New results on noncommutative and commutative polynomial identity testing
 In IEEE Conference on Computational Complexity
, 2008
"... Using ideas from automata theory we design a new efficient (deterministic) identity test for the noncommutative polynomial identity testing problem (first introduced and studied in [RS05, BW05]). More precisely, given as input a noncommutative circuit C(x1, · · · , xn) computing a polynomial in F ..."
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Cited by 12 (3 self)
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Using ideas from automata theory we design a new efficient (deterministic) identity test for the noncommutative polynomial identity testing problem (first introduced and studied in [RS05, BW05]). More precisely, given as input a noncommutative circuit C(x1, · · · , xn) computing a polynomial
Arithmetic Circuits and the Hadamard Product of Polynomials
 LIPICS LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS
, 2009
"... Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also give applications and connections to polynomial identity testing. Our main results are the following. • We show that no ..."
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Cited by 7 (1 self)
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that noncommutative polynomial identity testing for algebraic branching programs over rationals is complete for the logspace counting class C=L, and over fields of characteristic p the problem is in ModpL/poly. • We show an exponential lower bound for expressing the RazYehudayoff polynomial as the Hadamard product
Deterministic polynomial identity testing in non commutative models
 Computational Complexity
, 2004
"... We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: 1. Non Commutative Arithmetic Formulas: The algorithm gets as an input an arithmetic formula in the noncommuting variables x1,..., xn and determines whether or not the output of the formula ..."
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Cited by 54 (10 self)
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We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: 1. Non Commutative Arithmetic Formulas: The algorithm gets as an input an arithmetic formula in the noncommuting variables x1,..., xn and determines whether or not the output
Derandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds (Extended Abstract)
, 2003
"... Since Polynomial Identity Testing is a coRP problem, we obtain the following corollary: If RP = P (or, even, coRP ` "ffl?0NTIME(2nffl), infinitely often), then NEXP is not computable by polynomialsize arithmetic circuits. Thus, establishing that RP = coRP or BPP = P would require proving s ..."
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Cited by 175 (5 self)
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Since Polynomial Identity Testing is a coRP problem, we obtain the following corollary: If RP = P (or, even, coRP ` "ffl?0NTIME(2nffl), infinitely often), then NEXP is not computable by polynomialsize arithmetic circuits. Thus, establishing that RP = coRP or BPP = P would require proving
Progress on Polynomial Identity Testing
"... Polynomial identity testing (PIT) is the problem of checking whether a given arithmetic circuit is the zero circuit. PIT ranks as one of the most important open problems in the intersection of algebra and computational complexity. In the last few years, there has been an impressive progress on this ..."
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Cited by 16 (3 self)
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Polynomial identity testing (PIT) is the problem of checking whether a given arithmetic circuit is the zero circuit. PIT ranks as one of the most important open problems in the intersection of algebra and computational complexity. In the last few years, there has been an impressive progress
A nichtnegativstellensatz for polynomials in noncommuting variables
 Israel J. Math
"... Abstract. Let S ∪ {f} be a set of symmetric polynomials in noncommuting variables. If f satisfies a polynomial identity P i h i fhi = 1 + ..."
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Cited by 11 (7 self)
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Abstract. Let S ∪ {f} be a set of symmetric polynomials in noncommuting variables. If f satisfies a polynomial identity P i h i fhi = 1 +
Classifying polynomials and identity testing
, 2009
"... email: One of the fundamental problems of computational algebra is to classify polynomials according to the hardness of computing them. Recently, this problem has been related to another important problem: Polynomial identity testing. Informally, the problem is to decide if a certain succinct repre ..."
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Cited by 8 (1 self)
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email: One of the fundamental problems of computational algebra is to classify polynomials according to the hardness of computing them. Recently, this problem has been related to another important problem: Polynomial identity testing. Informally, the problem is to decide if a certain succinct
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