相关论文: Time and Space Bounds for Reversible Simulation

Greedy-GQ with linear function approximation, originally proposed in \cite{maei2010toward}, is a value-based off-policy algorithm for optimal control in reinforcement learning, and it has a non-linear two timescale structure with the…

Opacity is a property of privacy and security applications asking whether, given a system model, a passive intruder that makes online observations of system's behaviour can ascertain some "secret" information of the system. Deciding opacity…

We present new results on the landscape of problems that can be solved by quantum Turing machines (QTM's) employing severely limited amounts of memory. In this context, we demonstrate two infinite time hierarchies of complexity classes…

The Subspace Theorem is a powerful tool in number theory. It has appeared in various forms and been adapted and improved over time. It's applications include diophantine approximation, results about integral points on algebraic curves and…

Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…

This work theoretically studies a ubiquitous reinforcement learning policy for controlling the canonical model of continuous-time stochastic linear-quadratic systems. We show that randomized certainty equivalent policy addresses the…

We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…

The technique of Schroeppel and Shamir (SICOMP, 1981) has long been the most efficient way to trade space against time for the SUBSET SUM problem. In the random-instance setting, however, improved tradeoffs exist. In particular, the…

Reinforcement learning algorithms are usually stated without theoretical guarantees regarding their performance. Recently, Jin, Yang, Wang, and Jordan (COLT 2020) showed a polynomial-time reinforcement learning algorithm (namely, LSVI-UCB)…

We study the limitations for defining spatial and temporal intervals when the only available reference frame is a single composite quantum system, whose internal degrees of freedom serve as a temporal reference, a clock, and whose center of…

Time-reversal symmetry allows waves to retrace their paths through complex media and refocus at their origin. However, incomplete capture and reversal of scattered waves often limits pulse recompression. We address this challenge for…

In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform H\"older continuity in time, and strong convergence rates for a class of fully discrete exponential Euler-type numerical…

A method to compute guaranteed lower bounds to the eigenvalues of the Maxwell system in two or three space dimensions is proposed as a generalization of the method of Liu and Oishi [SIAM J. Numer. Anal., 51, 2013] for the Laplace operator.…

The evolution of an isolated quantum system inevitably exhibits recurrence: the state returns to the vicinity of its initial condition after finite time. Despite its fundamental nature, a rigorous quantitative understanding of recurrence…

In the field of reinforcement learning there has been recent progress towards safety and high-confidence bounds on policy performance. However, to our knowledge, no practical methods exist for determining high-confidence policy performance…

In this article, we analyze three classes of time-reversal of a Markov process with Gaussian noise on a manifold. We first unveil a commutativity constraint for the most general of these time-reversals to be well defined. Then we give a…

In this paper, we study the polyhedral structure of an integrated minimum-up/-down time and ramping polytope, which has broad applications in variant industries. The polytope we studied includes minimum-up/-down time, generation…

An extrinsic time is identified in most isotropic and homogeneous cosmological models by matching them with the ideal clock - a parametrized system whose only "degree of freedom" is time -. Once this matching is established, the…

Variational quantum time evolution allows us to simulate the time dynamics of quantum systems with near-term compatible quantum circuits. Due to the variational nature of this method the accuracy of the simulation is a priori unknown. We…

We critically discuss the measure of very short time intervals. By means of a "gedankenexperiment", we describe an ideal clock based on the occurrence of completely random events. We show that the minimum time interval Delta t that this…