Related papers: On the formalization of Asynchronous First Passage…
The paper aims to establish a convenient formal framework for investigating the phenomenon of scheme definiteness, exemplified by first-order internal categoricity as studied by V\"a\"an\"anen, among others. To this end, we introduce the…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
We propose a formalization of generic algorithms that includes analog algorithms. This is achieved by reformulating and extending the framework of abstract state machines to include continuous-time models of computation. We prove that every…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer…
The problem of initializing phase in a quantum computing system is considered. The initialization of phases is a problem when the system is initially present in an entangled state and also in the application of the quantum gate…
We introduce a transformation system for concurrent constraint programming (CCP). We define suitable applicability conditions for the transformations which guarantee that the input/output CCP semantics is preserved also when distinguishing…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
We study the question of whether the "termination with probability 1" property of a randomized algorithm is preserved when one replaces the atomic registers that the algorithm uses with linearizable (implementations of) registers. We show…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
We separate the criticisms of Hodges \cite{Hodges2005} and others into those against the algorithm itself and those against its physical implementation. We then point out that {\em all} those against the algorithm are either misleading or…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
Transformers have become the foundational architecture for a broad spectrum of sequence modeling applications, underpinning state-of-the-art systems in natural language processing, vision, and beyond. However, their theoretical limitations…
After highlighting the cases in which the semantics of a language cannot be mechanically reproduced (in which case it is called inherent), the main epistemological consequences of the first incompleteness Theorem for the two fundamental…
We study the problem of automated mechanism design with partial verification, where each type can (mis)report only a restricted set of types (rather than any other type), induced by the principal's limited verification power. We prove…
Motivated by large-scale optimization problems arising in the context of machine learning, there have been several advances in the study of asynchronous parallel and distributed optimization methods during the past decade. Asynchronous…
We identify a strong structural obstruction to Uniform Separation in constructive arithmetic. The mechanism is independent of semantic content; it emerges whenever two distinct evaluator predicates are sustained in parallel and inference…