Related papers: Geometric Model Checking of Continuous Space
Recognizing precise geometrical configurations of groups of objects is a key capability of human spatial cognition, yet little studied in the deep learning literature so far. In particular, a fundamental problem is how a machine can learn…
We consider the quantifier-free languages, Bc and Bc0, obtained by augmenting the signature of Boolean algebras with a unary predicate representing, respectively, the property of being connected, and the property of having a connected…
Comparative analysis of scalar fields is an important problem with various applications including feature-directed visualization and feature tracking in time-varying data. Comparing topological structures that are abstract and succinct…
Model checking approaches can be divided into two broad categories: global approaches that determine the set of all states in a model M that satisfy a temporal logic formula f, and local approaches in which, given a state s in M, the…
Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly…
Loop closure is necessary for correcting errors accumulated in simultaneous localization and mapping (SLAM) in unknown environments. However, conventional loop closure methods based on low-level geometric or image features may cause high…
Live sequence charts (LSCs) have been proposed as an inter-object scenario-based specification and visual programming language for reactive systems. In this paper, we introduce a logic-based framework to check the consistency of an LSC…
This paper introduces a novel generalization of the classical concept of $S$-metric spaces, referred to as composed $S$-metric spaces. By incorporating a composed function, we impose more general conditions on the triangle inequality,…
Humans naturally possess the spatial reasoning ability to form and manipulate images and structures of objects in space. There is an increasing effort to endow Vision-Language Models (VLMs) with similar spatial reasoning capabilities.…
3D spatial understanding is essential in real-world applications such as robotics, autonomous vehicles, virtual reality, and medical imaging. Recently, Large Language Models (LLMs), having demonstrated remarkable success across various…
The two major systems of formal verification are model checking and algebraic model-based testing. Model checking is based on some form of temporal logic such as linear temporal logic (LTL) or computation tree logic (CTL). One powerful and…
Comparison of geometric quantities usually means obtaining generally true equalities of different algebraic expressions of a given geometric figure. Today's technical possibilities already support symbolic proofs of a conjectured theorem,…
Spatial confounding is a persistent challenge in spatial statistics, influencing the validity of statistical inference in models that analyze spatially-structured data. The concept has been interpreted in various ways but is broadly defined…
Semantic scene completion is the task of jointly estimating 3D geometry and semantics of objects and surfaces within a given extent. This is a particularly challenging task on real-world data that is sparse and occluded. We propose a scene…
Inferring geometrically consistent dense 3D scenes across a tuple of temporally consecutive images remains challenging for self-supervised monocular depth prediction pipelines. This paper explores how the increasingly popular transformer…
The prime objective of this paper is to develop the notion of absolute continuity of functions on a more general setting outside $\R$. For this we have considered a topological space which is a measure space as well. We have built axioms…
The aim of this paper is to propose a geometric framework for modelling similarity search in large and multidimensional data spaces of general nature, which seems to be flexible enough to address such issues as analysis of complexity,…
Model checking allows one to automatically verify a specification of the expected properties of a system against a formal model of its behaviour (generally, a Kripke structure). Point-based temporal logics, such as LTL, CTL, and CTL*, that…
SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition…
Latent space models assume that network ties are more likely between nodes that are closer together in an underlying latent space. Euclidean space is a popular choice for the underlying geometry, but hyperbolic geometry can mimic more…