Showing papers in "Journal of Complexity in 1992"

TL;DR: The problem is to evaluate the complexity of solving the equation to a given accuracy, i.e., given a class 2l of instances, to point out the best possible upper bound of the number of calls of the oracle sufficient to find an e-solution to each of the instances.

TL;DR: It is shown that all presented algorithms are polynomial in the number of minterms occurring in the canonical disjunctive normal form representation of a Boolean function.

TL;DR: A problem that is not known to be solvable in polynomial time on a Turing machine, but can be solved on a unit-cost algebraic RAM with operations {+,-,∗,/,<}, and without the integer division operation is presented.

TL;DR: For a class of real machines using only linear functionals as computations and equality-tests, it is shown that the classes P and NP differ.

TL;DR: Theoretical results to obtain optimal or almost optimal sample points, optimal algorithms, and average case complexity functions for linear multivariate problems equipped with the folded Wiener sheet measure are applied.

TL;DR: A general lower bound involving Gaussian measures is proved in Monte Carlo approximation of linear operators and for Sobolev embeddings the rates of such approximation are determined.

TL;DR: A finite time version of the shadowing theorem is used to develop a procedure to determine the accuracy of numerically computed orbits of one-dimensional maps.

TL;DR: The main result is the characterization of n-widths in the case of linear operators in Hilbert spaces in Monte Carlo methods or randomized methods for linear operators.

TL;DR: A classical subject in computational complexity is what is usually called algebraic complexity, where R is a ring, understood as the number of ring operations the algorithm performs as a function of IZ, and the main kind of results are both upper and lower bounds.

TL;DR: A weakly numerically stable algorithm that numerically inverts an n × n well-conditioned Toeplitz matrix A in sequential time O( n log4 n log log n) or in parallel time of O(log3 n) using O(n log n loglog n) processors.

TL;DR: An optimal lower bound is proved on the number of additions, subtractions, and comparisons that are needed to decide membership in a generic hypersurface X ⊂ C m and over the reals, an analogous statement for irreducible “generic” hypersurfaces X⊂ R m is proved.

TL;DR: The exact order of the e-complexity in a power scale for some class of equations z = Hz + f in Hilbert space is found for classes of Fredholm equations, Volterra equations, and weakly singular integral equations.

TL;DR: It is proved that any LMP which satisfies (A.1) of Part I is tractable and its exponent is at most 2.1, and it is shown that optimal or nearly optimal sample points can be derived from hyperbolic cross points, and exhibit nearly optimal algorithms.

TL;DR: This work gives a linear-time algorithm that finds all occurrences of a pattern of length m in a text of length n in [formula] comparisons and establishes that, in general, searching for a long pattern is easier than searched for a short one.

TL;DR: The average error with respect to the noise and r-fold Wiener measure on the function space is considered and it is shown that for r = 0 the nth minimal error is asymptotically equal to 1 √6n + p( σ 2 (4n) ) 1 4 where1 √3 ≤ p, q ≤ 1 .

TL;DR: The problem of recovery values of the operator y = Ax with the help of discrete information which is taken from the element x is formulated, and concrete situations are considered where A is the mth differentiation operator or the convolution operator.

TL;DR: It is shown that the (e, α)-verification complexity is roughly equal to the η-computation complexity, where η = η( e, α) = Θ(eαr), where r depends on the problem norm, r ϵ [0, 1].

TL;DR: The probabilistic complexity of verification is studied as a function of the error tolerance e and the probability of failure δ for a linear continuous functional defined on a Banach space equipped with a Gaussian measure.

TL;DR: It is proved that there exist real numbers x and y such that x has a polynomial-time computable Cauchy function but its best fractions are not polynomially computable.

TL;DR: This paper proposes a more general approach by permitting a posteriori bounds to the probabilistic setting for approximately solved problems, and lets bounds Bcf, in addition to algorithms.

TL;DR: Improvements of estimates previously obtained by Burchard and Hollig and by Stenger of the Kolmogorov n-widths, Gel'fand n- widths dn, and linear n-Widths δn of the Hardy spaces Hp in Lq(−1, 1) are estimated.

TL;DR: In this paper, the exact solutions of the L∝ norm on some classes of monosplines with free knots on the real axis are obtained, and the optimal quadrature formula and optimal error on the convolution class taking a PF density as its kernal are given.

TL;DR: This paper represents an approach to the problem of average characteristics, which was connected with the notion of “average entropy,” and calculates average and a-average dimensions of some classes of functions on R.

TL;DR: The Theorem of Kharitonov with the Test of Routh is combined and it is shown that the number of elementary operations required for the solution of the robust stability problem is at most O(n2).

TL;DR: This paper verifies the conjecture that if the Anosov endomorphism is non-expanding, then the branch structure may be eliminated via shift equivalence under an additional assumption that the branchructure has no crossings.

TL;DR: It is shown that generating a minimum-cost synchronizable test sequence is an NP-hard problem and that designing an s-approximation algorithm for the problem is at least as hard as designing an e-app approximator for the asymmetric traveling salesman problem obeying the triangle inequality.