Related papers: Computing with and without arbitrary large numbers
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
Random numbers play a crucial role in science and industry. Many numerical methods require the use of random numbers, in particular the Monte Carlo method. Therefore it is of paramount importance to have efficient random number generators.…
Voltage peaks on a conventional computer's power lines allow for the well-known dangerous DPA attacks. We show that measurement of a quantum computer's transient state during a computational step reveals information about a complete…
Recent investigations show insertion-deletion systems of small size that are not complete and cannot generate all recursively enumerable languages. However, if additional computational distribution mechanisms like P systems are added, then…
Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…
The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity…
Simon's classical random-copying model, introduced in 1955, has garnered much attention for its ability, in spite of an apparent simplicity, to produce characteristics similar to those observed across the spectrum of complex systems.…
For any pair $(X,Z)$ of correlated random variables we can think of $Z$ as a randomized function of $X$. Provided that $Z$ is short, one can make this function computationally efficient by allowing it to be only approximately correct. In…
Resistive random-access memory (RRAM) is gaining popularity due to its ability to offer computing within the memory and its non-volatile nature. The unique properties of RRAM, such as binary switching, multi-state switching, and device…
Quantum devices can process data in a fundamentally different way than classical computers. To leverage this potential, many algorithms require the aid of a quantum Random Access Memory (QRAM), i.e. a module capable of efficiently loading…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
We obtain a new bound on exponential sums over integers without large prime divisors, improving that of Fouvry and Tenenbaum (1991). For a fixed integer $\nu\ne 0$, we also obtain new bounds on exponential sums with $\nu$-th powers of such…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
In the classical RAM, we have the following useful property. If we have an algorithm that uses $M$ memory cells throughout its execution, and in addition is sparse, in the sense that, at any point in time, only $m$ out of $M$ cells will be…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…
We characterize some major algorithmic randomness notions via differentiability of effective functions. (1) As the main result we show that a real number z in [0,1] is computably random if and only if each nondecreasing computable function…