Related papers: Counting is Easy
This paper describes the formal verification of two Turing machines using the program verifier Dafny. Both machines are deciders, so we prove total correctness. They are typical first examples of Turing machines used in any course of…
The present work determines the exact nature of {\em linear time computable} notions which characterise automatic functions (those whose graphs are recognised by a finite automaton). The paper also determines which type of linear time…
The generation of random numbers is a task of paramount importance in modern science. A central problem for both classical and quantum randomness generation is to estimate the entropy of the data generated by a given device. Here we present…
In this paper, we consider the problem of generalised visual object counting, with the goal of developing a computational model for counting the number of objects from arbitrary semantic categories, using arbitrary number of "exemplars",…
The fixed point construction is a method for designing tile sets and cellular automata with highly nontrivial dynamical and computational properties. It produces an infinite hierarchy of systems where each layer simulates the next one. The…
This article presents numerical recipes for simulating high-temperature and non-equilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass…
The paper is devoted to a new idea of simulation of accounting by quantum computing. We expose the actual accounting principles in a pure mathematics language. After that we simulated the accounting principles on quantum computers. We show…
We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values…
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…
We show, within the circuit model, how any quantum computation can be efficiently performed using states with only real amplitudes (a result known within the Quantum Turing Machine model). This allows us to identify a 2-qubit (in fact…
A possibility of performing the C-NOT gate operation at the ground and the first excited states of two harmonic oscillators interacting via a two-level system subject to complete control is demonstrated. The system resembles Turing machine,…
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the…
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in…
World models provide a powerful framework for simulating environment dynamics conditioned on actions or instructions, enabling downstream tasks such as action planning or policy learning. Recent approaches leverage world models as learned…
This paper goes back to Turing (1936) and treats his machine as a cognitive model (W,D,B), where W is an "external world" represented by memory device (the tape divided into squares), and (D,B) is a simple robot that consists of the…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
Pseudo-random number generators (PRNGs) are essential in a wide range of applications, from cryptography to statistical simulations and optimization algorithms. While uniform randomness is crucial for security-critical areas like…
Quantum computer is the key to controlling complex processes. If its hardware, in general is successfully created on the basis of the physical baggage of the 20th century, the mathematical software is fundamentally lagging behind. Feynman's…
This work studies some aspects of the computational power of fully asynchronous cellular automata (ACA). We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences…
This paper is a primer on cryptographic accumulators and how to apply them practically. A cryptographic accumulator is a space- and time-efficient data structure used for set-membership tests. Since it is possible to represent any…