Related papers: Bisimulation maps in presheaf categories
Hasse diagrams provide a principled means for visualizing the structure of statistical designs constructed by crossing and nesting of experimental factors. They have long been applied for automated construction of linear models and their…
We propose a modal study of the notion of bisimulation. Our contribution is threefold. First, we extend the basic modal language with a new modality $\nbi$, whose intended meaning is universal quantification over all states that are…
The problem of finding a finite state symbolic model which is bisimilar to a hybrid dynamical system (HDS) and has the minimum number of states is considered. The considered class of HDS allows for discrete-valued inputs that only affect…
Symbols representing abstract states such as "dish in dishwasher" or "cup on table" allow robots to reason over long horizons by hiding details unnecessary for high-level planning. Current methods for learning to identify symbolic states in…
We introduce a Bredon motivic cohomology theory for smooth schemes defined over a field and equipped with an action by a finite group. These cohomology groups are defined for finite dimensional representations as the hypercohomology of…
The behavior and architecture of large scale discrete state systems found in computer software and hardware can be specified and analyzed using a particular class of primitive recursive functions. This paper begins with an illustration of…
In recent years, domains such as natural language processing and image recognition have popularized the paradigm of using large datasets to pretrain representations that can be effectively transferred to downstream tasks. In this work we…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
Category, or property generalization is a central function in the human cognition. It plays a crucial role in a variety of domains, such as learning, everyday reasoning, specialized reasoning, and decision making. Judging the content of a…
We extend the notion of a factorization system in a category to the realm of $\infty$-categories. To this end, we provide a description of the category of $\infty$-categories with factorization systems as the category of presheaves of…
Labeled state-to-function transition systems, FuTS for short, admit multiple transition schemes from states to functions of finite support over general semirings. As such they constitute a convenient modeling instrument to deal with…
Bigraph reactive systems offer a powerful and flexible mathematical framework for modelling both spatial and non-spatial relationships between agents, with practical applications in domains such as smart technologies, networks, sensor…
Several application domains require formal but flexible approaches to the comparison problem. Different process models that cannot be related by behavioral equivalences should be compared via a quantitative notion of similarity, which is…
We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
This chapter explores dynamical structural equation models (DSEMs) and their nonlinear generalizations into sheaves of dynamical systems. It demonstrates these two disciplines on part of the food web in the Bering Sea. The translation from…
State machine formalisms equipped with hierarchy and parallelism allow to compactly model complex system behaviours. Such models can then be transformed into executable code or inputs for model-based testing and verification techniques.…
Efficient planning in continuous state and action spaces is fundamentally hard, even when the transition model is deterministic and known. One way to alleviate this challenge is to perform bilevel planning with abstractions, where a…
This is the third installment in a series of papers on algebraic set theory. In it, we develop a uniform approach to sheaf models of constructive set theories based on ideas from categorical logic. The key notion is that of a "predicative…