Related papers: On the Impossibility of a Perfect Hypervisor
We look at what type of arguments can rule out the joint reality (or value definiteness) of two observables of a physical system, such as a qubit, and give several strong yet simple no-go results based on assumptions typically weaker than…
We consider the online problem of scheduling jobs on identical machines, where jobs have precedence constraints. We are interested in the demanding setting where the jobs sizes are not known up-front, but are revealed only upon completion…
Universality results for equivariant neural networks remain rare. Those that do exist typically hold only in restrictive settings: either they rely on regular or higher-order tensor representations, leading to impractically high-dimensional…
By the sometimes so-called 'Main Theorem' of Recursive Analysis, every computable real function is necessarily continuous. We wonder whether and which kinds of HYPERcomputation allow for the effective evaluation of also discontinuous…
We introduce a new consistency-based approach for defining and solving nonnegative/positive matrix and tensor completion problems. The novelty of the framework is that instead of artificially making the problem well-posed in the form of an…
Diagnosability is a system theoretical property characterizing whether fault occurrences in a system can always be detected within a finite time. In this paper, we investigate the verification of diagnosability for cyber-physical systems…
Given a sound first-order p-time theory $T$ capable of formalizing syntax of first-order logic we define a p-time function $g_T$ that stretches all inputs by one bit and we use its properties to show that $T$ must be incomplete. We leave it…
The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one hand we confirm that the classification problems for…
This essay aims to propose construction theory, a new domain of theoretical research on machine construction, and use it to shed light on a fundamental relationship between living and computational systems. Specifically, we argue that…
In this paper, we study the observability of compactly perturbed infinite dimensional systems. Assuming that a given infinite-dimensional system with self-adjoint generator is exactly observable we derive sufficient conditions on a compact…
The inferential model (IM) framework produces data-dependent, non-additive degrees of belief about the unknown parameter that are provably valid. The validity property guarantees, among other things, that inference procedures derived from…
In a recent provocative paper, Lamport points out "the insubstantiality of processes" by proving the equivalence of two different decompositions of the same intuitive algorithm by means of temporal formulas. We point out that the correct…
Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preventing the full development of this promising theory. In this…
We prove that there is no algorithm to decide whether a given integer vector is in the closure of the entropic cone $\overline{\Gamma_{n}^{*}}$. Equivalently, there is no decision procedure to determine whether a given integer-valued…
Hyperproperties, as introduced by Clarkson and Schneider, characterize the correctness of a computer program as a condition on its set of computation paths. Standard temporal logics can only refer to a single path at a time, and therefore…
No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no-go arguments against non-contextual hidden variables. All such arguments rely on choosing special sets of quantum-mechanical…
It is well-known that a strict analogue of the Birkhoff Ergodic Theorem in infinite ergodic theory is trivial; it states that for any infinite-measure-preserving ergodic system the Birkhoff average of every integrable function is almost…
Foundational models of computation often abstract away physical hardware limitations. However, in extreme environments like In-Network Computing (INC), these limitations become inviolable laws, creating an acute trilemma among communication…
Let $X$ be an arbitrary set. Then a topology $t$ on $X$ is said to be completely useful if every upper semicontinuous linear (total) preorder $\precsim$ on $X$ can be represented by an upper semicontinuous real-valued order preserving…
Formal verification provides strong safety guarantees but only for models of cyber-physical systems. Hybrid system models describe the required interplay of computation and physical dynamics, which is crucial to guarantee what computations…