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418
Indexing StraightLine Programs
, 2008
"... Straightline programs offer powerful text compression by representing a text T[1, u] in terms of a contextfree grammar of n rules, so that T can be recovered in O(u) time. However, the problem of operating the grammar in compressed form has not been studied much. We present the first grammar repre ..."
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Straightline programs offer powerful text compression by representing a text T[1, u] in terms of a contextfree grammar of n rules, so that T can be recovered in O(u) time. However, the problem of operating the grammar in compressed form has not been studied much. We present the first grammar
Factorization of Polynomials Given by StraightLine Programs
 Randomness and Computation
, 1989
"... An algorithm is developed for the factorization of a multivariate polynomial represented by traightline program into its irreducible factors. The algorithm is in random polynomialtime as a function in the input size, total degree, and binary coefficient length for the usual coefficient fields and ..."
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Cited by 34 (8 self)
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and outputs a straightline program, which with controllably high probability correctly determines the irreducible factors. It also returns the probably correct multiplicities of each distinct factor. If th oefficient field has finite characteristic p and p divides the multiplicities of some irreducible
Straightline programs in geometric elimination theory
 J. Pure Appl. Algebra
, 1998
"... Dedicated to Volker Strassen for his work on complexity We present a new method for solving symbolically zero–dimensional polynomial equation systems in the affine and toric case. The main feature of our method is the use of problem adapted data structures: arithmetic networks and straight–line prog ..."
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Cited by 64 (16 self)
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” of the equation system. Here, the input is thought to be given by a straight–line program (or alternatively in sparse representation), and the length of the input is measured by number of variables, degree of equations and size of the program (or sparsity of the equations). The geometric degree of the input
Straightline Programs in Polynomial Equation Solving
, 2002
"... Solving symbolically polynomial equation systems when all polynomials are represented in the usual dense encoding turns out to be very inefficient: the sizes of the systems one can deal with do not respond to realistic needs. Evaluation representations appeared a decade ago in this frame as an alte ..."
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Cited by 2 (0 self)
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as an alternative to classify families of problems which behave better with respect to complexity. We present a survey of the most recent complexity results for different polynomial problems when the input is encoded by evaluation (straightline) programs. We also show how surprising mathematical byproducts
Greatest Common Divisors of Polynomials Given by StraightLine Programs
 J. ACM
, 1988
"... . F Algorithms on multivariate polynomials represented by straightline programs are developed irst it is shown that most algebraic algorithms can be probabilistically applied to data that is given by y r a straightline computation. Testing such rational numeric data for zero, for instance, is faci ..."
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Cited by 55 (18 self)
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. F Algorithms on multivariate polynomials represented by straightline programs are developed irst it is shown that most algebraic algorithms can be probabilistically applied to data that is given by y r a straightline computation. Testing such rational numeric data for zero, for instance
Implicit Computation: An Output Polynomial Algorithm for Evaluating StraightLine Programs
, 1999
"... theory of computation, randomized algorithms, straightline programs, outputpolynomial algorithms Inputless straightline programs using addition, subtraction and multiplication are considered. An outputpolynomial algorithm is given for computing the output of such a program. The program runs in t ..."
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theory of computation, randomized algorithms, straightline programs, outputpolynomial algorithms Inputless straightline programs using addition, subtraction and multiplication are considered. An outputpolynomial algorithm is given for computing the output of such a program. The program runs
Probabilistic algorithms for deciding equivalence of straightline programs
 J. ACM
, 1983
"... Let Q be any algebraic structure and ~the set of all total programs over Q using the instruction set {z,, 1, z,, x + y, z,, x y, z ~ x * y, z ~ x/y}. (A program is total if no division by zero occurs during any computation) Let the equivalence problem for ~ be the problem of deciding for tw ..."
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Cited by 48 (1 self)
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Let Q be any algebraic structure and ~the set of all total programs over Q using the instruction set {z,, 1, z,, x + y, z,, x y, z ~ x * y, z ~ x/y}. (A program is total if no division by zero occurs during any computation) Let the equivalence problem for ~ be the problem of deciding
A straight line program . . . (Extended Abstract)
"... While NC algorithms have been discovered for the basic arithmetic operations, the parallel complexity of some fundamental problems as integer gcd is still open, since first being raised in a paper of Cook [2]. Many authors attempt to design fast parallel integer GCD algorithms. Chor and Goldreich [1 ..."
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[1] proposed O(n / log n)ɛ parallel time with O(n 1+ɛ) number of processors, for any ɛ> 0. Sorenson [4] and the author [3] also suggest other parallel algorithms with the same parallel performance. Since then, no major improvements have been made. In this paper, we propose a straight line program
Results 1  10
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