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39
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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expression). One application is a deterministic polynomial time identity testing for setmultilinear arithmetic circuits of depth 3. We also give a deterministic polynomial time identity testing algorithm for noncommutative algebraic branching programs as defined by Nisan. Finally, we observe an exponential
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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sided error) and evaluates the circuit over the ring of matrices. In addition, we present query complexity lower bounds for identity testing and explore the possibility of derandomizing our algorithm. The analysis of our algorithm uses a noncommutative variant of the SchwartzZippel test. Minimizing algebraic
ALGEBRAIC ALGORITHMS1
, 2012
"... This is a preliminary version of a Chapter on Algebraic Algorithms in the up ..."
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This is a preliminary version of a Chapter on Algebraic Algorithms in the up
und Computeralgebra (CDC) Algebraic methods in analyzing lightweight cryptographic symmetric primitives
"... Algebraic methods in analyzing ..."
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
HITTINGSETS FOR ROABP AND SUM OF SETMULTILINEAR CIRCUITS
"... Abstract. We give a nO(logn)time (n is the input size) blackbox polynomial identity testing algorithm for unknownorder readonce oblivious arithmetic branching programs (ROABP). The best timecomplexity known for blackbox PIT for this class was nO(log 2 n) due to ForbesSaptharishiShpilka (STOC 2 ..."
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Cited by 1 (0 self)
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Abstract. We give a nO(logn)time (n is the input size) blackbox polynomial identity testing algorithm for unknownorder readonce oblivious arithmetic branching programs (ROABP). The best timecomplexity known for blackbox PIT for this class was nO(log 2 n) due to ForbesSaptharishiShpilka (STOC
Hittingsets for lowdistance multilinear depth3
"... Abstract. The depth3 model has recently gained much importance, as it has become a steppingstone to understanding general arithmetic circuits. Its restriction to multilinearity has known exponential lower bounds but no nontrivial blackbox identity tests. In this paper, we take a step towards desig ..."
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Abstract. The depth3 model has recently gained much importance, as it has become a steppingstone to understanding general arithmetic circuits. Its restriction to multilinearity has known exponential lower bounds but no nontrivial blackbox identity tests. In this paper, we take a step towards
Volume I: Computer Science and Software Engineering
, 2013
"... Algebraic algorithms deal with numbers, vectors, matrices, polynomials, formal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matrices and polynomials is fundamental for modern computations in Sc ..."
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Algebraic algorithms deal with numbers, vectors, matrices, polynomials, formal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matrices and polynomials is fundamental for modern computations
A Numerical Study of the Lorenz and LorenzStenflo Systems
"... ges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen ..."
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ges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen
Results 1  10
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