Related papers: $\mathrm{Pal}^k$ Is Linear Recognizable Online
We described a simple algorithm running in linear time for each fixed constant $k$, that either establishes that the pathwidth of a graph $G$ is greater than $k$, or finds a path-decomposition of $G$ of width at most $O(2^{k})$. This…
Linear conjunctive grammars are a family of formal grammars with an explicit conjunction operation allowed in the rules, which is notable for its computational equivalence fo one-way real-time cellular automata, also known as trellis…
In the Interval Completion problem we are given a graph G and an integer k, and the task is to turn G using at most k edge additions into an interval graph, i.e., a graph admitting an intersection model of intervals on a line. Motivated by…
Infinite Time Register Machines ($ITRM$'s) are a well-established machine model for infinitary computations. Their computational strength relative to oracles is understood, see e.g. Koepke (2009), Koepke and Welch (2011) and Koepke and…
Interval and proper interval graphs are very well-known graph classes, for which there is a wide literature. As a consequence, some generalizations of interval graphs have been proposed, in which graphs in general are expressed in terms of…
Consider an independent site percolation model on $\Z^d$, with parameter $p \in (0,1)$, where all long range connections in the axes directions are allowed. In this work we show that given any parameter $p$, there exists and integer $K(p)$…
Our paper investigates the linear logic of knowledge and time LTK_r with reflexive intransitive time relation. The logic is defined semantically, -- as the set of formulas which are true at special frames with intransitive and reflexive…
We propose a novel online learning algorithm, called SpCoSLAM 2.0, for spatial concepts and lexical acquisition with high accuracy and scalability. Previously, we proposed SpCoSLAM as an online learning algorithm based on unsupervised…
We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…
We describe a formal correctness proof of RANKING, an online algorithm for online bipartite matching. An outcome of our formalisation is that it shows that there is a gap in all combinatorial proofs of the algorithm. Filling that gap…
Mixed linear regression (MLR) is a powerful model for characterizing nonlinear relationships by utilizing a mixture of linear regression sub-models. The identification of MLR is a fundamental problem, where most of the existing results…
Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…
Language Identification (LI) is an important first step in several speech processing systems. With a growing number of voice-based assistants, speech LI has emerged as a widely researched field. To approach the problem of identifying…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
As an essential component of visual simultaneous localization and mapping (SLAM), place recognition is crucial for robot navigation and autonomous driving. Existing methods often formulate visual place recognition as feature matching, which…
We introduce a family of novel ranking algorithms called ERank which run in linear/near linear time and build on explicitly modeling a network as uncertain evidence. The model uses Probabilistic Argumentation Systems (PAS) which are a…
Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the…
An unweighted, undirected graph $G$ on $n$ nodes is said to have \emph{bandwidth} at most $k$ if its nodes can be labelled from $0$ to $n - 1$ such that no two adjacent nodes have labels that differ by more than $k$. It is known that one…
Large Language Models (LLMs) have achieved human-level proficiency across diverse tasks, but their ability to perform rigorous mathematical problem solving remains an open challenge. In this work, we investigate a fundamental yet…