Related papers: The physical limit of logical compare operation
Using a recursive approach, we obtain a simple exact expression for the L^2-distance from the limit in R\'egnier's (1989) classical limit theorem for the number of key comparisons required by QuickSort. A previous study by Fill and Janson…
Temporal Equilibrium Logic (TEL) is a promising framework that extends the knowledge representation and reasoning capabilities of Answer Set Programming with temporal operators in the style of LTL. To our knowledge it is the first…
Maxwell's demon is a famous thought experiment and a paradigm of the thermodynamics of information. It is related to Szilard's engine, a two-state information-to-work conversion device in which the demon performs single measurements and…
We consider the problem of sorting $n$ items, given the outcomes of $m$ pre-existing comparisons. We present a simple and natural deterministic algorithm that runs in $O(m + \log T)$ time and does $O(\log T)$ comparisons, where $T$ is the…
It is known [DemriSchnoebelen02] that both satisfiability and model-checking problems for propositional Linear-time Temporal Logic, LTL, with only a single propositional variable in the language are PSPACE-complete, which coincides with the…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
Motivated by settings such as medical treatments or aircraft maintenance, we consider a scheduling problem with jobs that consist of two operations, a test and a processing part. The time required to execute the test is known in advance…
This work provides an overview of key historical developments in the formulation of the Second Law of Thermodynamics, focusing on the notorious challenge of ``Maxwell's Demon'', a hypothetical creature who could presumably violate that law.…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…
The ability to measure the stochastic degrees of freedom of a thermal system enables the extraction of energy from an equilibrium heat bath. This is the underlying principle of Maxwell's demon and subsequent information engines. Here, we…
We revisit two well-studied scheduling problems in the unrelated machines setting where each job can have a different processing time on each machine. For minimizing total weighted completion time we give a 1.45-approximation, which…
We report an experimental realisation of Maxwell's demon in a photonic setup. We show that a measurement at the single-photon level followed by a feed-forward operation allows the extraction of work from intense thermal light into an…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
We introduce a family of Generalized Continuous Maxwell Demons (GCMDs) operating on idealized single-bit equilibrium devices that combine the single-measurement Szilard and the repeated measurements of the Continuous Maxwell Demon…
We study the complexity of high-dimensional approximation in the $L_2$-norm when different classes of information are available; we compare the power of function evaluations with the power of arbitrary continuous linear measurements. Here,…
We give a short proof that any comparison-based n^(1-epsilon)-approximation algorithm for the 1-dimensional Traveling Salesman Problem (TSP) requires Omega(n log n) comparisons.
We determine the complexity of second-order HyperLTL satisfiability, finite-state satisfiability, and model-checking: All three are equivalent to truth in third-order arithmetic. We also consider two fragments of second-order HyperLTL that…
While most of the existing quantum information engines assisted by Maxwell's demon harness thermal fluctuations, those that rectify only quantum fluctuations have recently been constructed. We propose an alternative type of quantum…
In multiprocessor systems, various problems are treated with Lamport's logical clock and the resultant logical time orders between operations. However, one often needs to face the high complexities caused by the lack of logical time order…
We derive a fundamental upper bound on the rate at which a device can process information (i.e., the number of logical operations per unit time), arising from quantum mechanics and general relativity. In Planck units a device of volume V…