Related papers: Extending Landauer's Bound from Bit Erasure to Arb…
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these…
A computational abstract machine based on two operations: referencing and bit copying is presented. These operations are sufficient for carrying out any computation. They can be used as the primitives for a Turing-complete programming…
We consider the minimal thermodynamic cost of an individual computation, where a single input $x$ is mapped to a single output $y$. In prior work, Zurek proposed that this cost was given by $K(x\vert y)$, the conditional Kolmogorov…
One of the outstanding challenges to information processing is the eloquent suppression of energy consumption in execution of logic operations. Landauer principle sets an energy constraint in deletion of a classical bit of information.…
When a computational task tolerates a relaxation of its specification or when an algorithm tolerates the effects of noise in its execution, hardware, programming languages, and system software can trade deviations from correct behavior for…
We present a simple, top-down approach for the calculation of minimum energy consumption of electrosorptive ion separation using variational form of the (Gibbs) free energy. We focus and expand on the case of electrostatic capacitive…
Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly…
We analyse the maximum achievable rate of sustained computation for a given convex region of three dimensional space subject to geometric constraints on power delivery and heat dissipation. We find a universal upper bound across both…
It was recently shown that a generalization of quantum Turing machines (QTMs), in which potentials are associated with elementary steps or transitions of the computation, generates potential distributions along computation paths of states…
It is often claimed, that from a quantum system of d levels, and entropy S and heat bath of temperature T one can draw kT(ln d -S) amount of work. However, the usual arguments based on Szilard engine are not fully rigorous. Here we prove…
Thermodynamics and information have intricate inter-relations. The justification of the fact that information is physical, is done by inter-linking information and thermodynamics - through Landauer's principle. This modern approach towards…
Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…
We analyze a token-based Brownian circuit in which Brownian particles, coined `tokens,' move randomly by exploiting thermal fluctuations, searching for a path in multi-token state space corresponding to the solution of a given problem. The…
We consider a model of computation motivated by possible limitations on quantum computers. We have a linear array of n wires, and we may perform operations only on pairs of adjacent wires. Our goal is to build a circuits that perform…
Limitation of computational resources is considered as a universal principle that for simulation is as fundamental as physical laws are. It claims that all experimentally verifiable implications of physical laws can be simulated by the…
We examine some variants of computation with closed timelike curves (CTCs), where various restrictions are imposed on the memory of the computer, and the information carrying capacity and range of the CTC. We give full characterizations of…
Landauer's erasure principle exposes an intrinsic relation between thermodynamics and information theory: the erasure of information stored in a system, S, requires an amount of work proportional to the entropy of that system. This entropy,…
Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour (finitely) executable if, and only if, it is equivalent to the behaviour of a (finite) reactive Turing…
The ultimate limits of computation are not just logical, but physical. We investigate the physical resources -- time, energy, entropy, and free energy -- required to perform computational work. We apply the resulting measures of physical…
Probabilistic circuits (PCs) offer a promising avenue to perform embedded reasoning under uncertainty. They support efficient and exact computation of various probabilistic inference tasks by design. Hence, hardware-efficient computation of…