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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
Relational Queries Computable in Polynomial Time
 Information and Control
, 1986
"... We characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe. We also show that even without the ordering one application of fixed point suffices to express any query expressible with several ..."
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Cited by 318 (17 self)
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We characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe. We also show that even without the ordering one application of fixed point suffices to express any query expressible
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 +
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
Comparing top k lists
 In Proceedings of the ACMSIAM Symposium on Discrete Algorithms
, 2003
"... Motivated by several applications, we introduce various distance measures between “top k lists.” Some of these distance measures are metrics, while others are not. For each of these latter distance measures, we show that they are “almost ” a metric in the following two seemingly unrelated aspects: ( ..."
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Cited by 272 (4 self)
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: (i) they satisfy a relaxed version of the polygonal (hence, triangle) inequality, and (ii) there is a metric with positive constant multiples that bound our measure above and below. This is not a coincidence—we show that these two notions of almost being a metric are formally identical. Based
ALGEBRAS, DIALGEBRAS, AND POLYNOMIAL IDENTITIES
 SERDICA MATH. J. 38 (2012), 91–136
, 2012
"... This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for conver ..."
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Cited by 4 (4 self)
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This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm
IdentityType Functions and Polynomials
, 2007
"... For a noncommuting product of functions, similar to convolutions, an “identitytype function ” leaving a specific function invariant is defined. It is evaluated for any choice of function on which it acts by solving a functional equation. A closedform representation for the identitytype function o ..."
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For a noncommuting product of functions, similar to convolutions, an “identitytype function ” leaving a specific function invariant is defined. It is evaluated for any choice of function on which it acts by solving a functional equation. A closedform representation for the identitytype function
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
Results 1  10
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2,893