Related papers: Efficient Computation by Three Counter Machines
As was initially shown by Brent, exponentials of truncated power series can be computed using a constant number of polynomial multiplications. This note gives a relatively simple algorithm with a low constant factor.
We prove the equivalence of two classes of counter machines and one class of distributed automata. Our counter machines operate on finite words, which they read from left to right while incrementing or decrementing a fixed number of…
We derive formulas which connect cumulants of particle numbers observed with efficiency losses with the original ones based on the binomial model. These formulas can describe the case with multiple efficiencies in a compact form. Compared…
We consider an expansion of Presburger arithmetic which allows multiplication by $k$ parameters $t_1,\ldots,t_k$. A formula in this language defines a parametric set $S_\mathbf{t} \subseteq \mathbb{Z}^{d}$ as $\mathbf{t}$ varies in…
We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.
In this expository paper we describe four primality tests. The first test is very efficient, but is only capable of proving that a given number is either composite or 'very probably' prime. The second test is a deterministic polynomial time…
We present an example of quantum computational tasks whose performance is enhanced if we distribute quantum information using quantum cloning. Furthermore we give achievable efficiencies for probabilistic cloning the quantum states used in…
We show that polynomial time Turing equivalence and a large class of other equivalence relations from computational complexity theory are universal countable Borel equivalence relations. We then discuss ultrafilters on the invariant Borel…
Matrix multiplication is integral to various scientific and engineering disciplines, including machine learning, image processing, and gaming. With the increasing data volumes in areas like machine learning, the demand for efficient…
A novel computing model, called \emph{Probe Machine}, is proposed in this paper. Different from Turing Machine, Probe Machine is a fully-parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview…
We design a recursive algorithm to compute the partition function of the Ising model, summed over cubic maps with fixed size and genus. The algorithm runs in polynomial time, which is much faster than methods based on a Tutte-like, or…
Recently, many techniques have been introduced that allow the (automated) classification of the runtime complexity of term rewrite systems (TRSs for short). In earlier work, the authors have shown that for confluent TRSs, innermost…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
We study the problem of computing matrix chain multiplications in a distributed computing cluster. In such systems, performance is often limited by the straggler problem, where the slowest worker dominates the overall computation latency.…
We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
This paper presents a method to analyze the powers of a given trilinear form (a special kind of algebraic constructions also called a tensor) and obtain upper bounds on the asymptotic complexity of matrix multiplication. Compared with…