Related papers: Non-deterministic approximation operators: ultimat…
Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…
This note has several aims. Firstly, it portrays a non-standard analysis as a functor, namely a functor * that maps any set A to the set *A of its non-standard elements. That functor, from the category of sets to itself, is postulated to be…
We shall generalize the concept of $z=(1-t)x\oplus ty$ to $n$ times which contains to verifying some their properties and inequalities in CAT(0) spaces. In the sequel with introducing of $\alpha$-nonexpansive mappings, we obtain some fixed…
Fixed-point equations with Lipschitz operators have been studied for more than a century, and are central to problems in mathematical optimization, game theory, economics, and dynamical systems, among others. When the Lipschitz constant of…
This work is a comparative study between the existence of fixed point for homomorphisms in a class of binary relationnal systems and the existence of fixed point for nonexpansive mappings in semimetric spaces.
A Fixed-Parameter Tractable (\FPT) $\rho$-approximation algorithm for a minimization (resp. maximization) parameterized problem $P$ is an FPT algorithm that, given an instance $(x, k)\in P$ computes a solution of cost at most $k \cdot…
Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration…
We propose a novel extension to symmetrized neural network operators by incorporating fractional and mixed activation functions. This study addresses the limitations of existing models in approximating higher-order smooth functions,…
Automatic term extraction (ATE) is a Natural Language Processing (NLP) task that eases the effort of manually identifying terms from domain-specific corpora by providing a list of candidate terms. As units of knowledge in a specific field…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
We introduce a novel architecture and computational framework for formal, automated analysis of systems with a broad set of nonlinearities in the feedback loop, such as neural networks, vision controllers, switched systems, and even simple…
We present a theoretical framework in which a document and an AI model engage in a transfinite fixed-point interaction that leads to stable semantic alignment. Building on the foundations of Alpay Algebra, we introduce a functorial system…
We study the map between two descriptions of the $T\bar{T}$ deformation of conformal field theory (CFT): One is the defining description as a deformation of CFT by the $T\bar{T}$-operator. The other is an alternative description as the…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…
This paper investigates the distributed fixed point finding problem for a global operator over a directed and unbalanced multi-agent network, where the global operator is quasinonexpansive and only partially accessible to each individual…
We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal…
We present a new partial order reduction method for reachability analysis of nondeterministic labeled transition systems over metric spaces. Nondeterminism arises from both the choice of the initial state and the choice of actions, and the…