Related papers: A zonotopic framework for functional abstractions
We are concerned with the question of how an agent can acquire its own representations from sensory data. We restrict our focus to learning representations for long-term planning, a class of problems that state-of-the-art learning methods…
This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these…
In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…
We introduce refinement in the function-behaviour-structure framework for design, as described by John Gero, in order to deal with complexity. We do this by connecting the frameworks for the design of two models, one the refinement of the…
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI.…
Abstract argumentation framework (\AFname) is a unifying framework able to encompass a variety of nonmonotonic reasoning approaches, logic programming and computational argumentation. Yet, efficient approaches for most of the decision and…
We present a sequent calculus for abstract focussing, equipped with proof-terms: in the tradition of Zeilberger's work, logical connectives and their introduction rules are left as a parameter of the system, which collapses the synchronous…
Transfer systems on finite posets have recently been gaining traction as a key ingredient in equivariant homotopy theory. Additionally, they also naturally occur in the data of a model structure. We give a complete characterization of all…
Developing suitable formal semantics can be of great help in the understanding, design and implementation of a programming language, and act as a guide for software development tools like analyzers or partial evaluators. In this sense, full…
Automated synthesis of reactive control protocols from temporal logic specifications has recently attracted considerable attention in various applications in, for example, robotic motion planning, network management, and hardware design. An…
Abstraction (in its various forms) is a powerful established technique in model-checking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an…
Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states…
We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…
We present a new approach for performing predicate abstraction based on symbolic decision procedures. Intuitively, a symbolic decision procedure for a theory takes a set of predicates in the theory and symbolically executes a decision…
In this paper, we introduce a compositional scheme for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on small-gain type reasoning. In…
Mechanisms are a fundamental concept in many areas of science. Nonetheless, there has been little effort to develop structures to represent mechanisms. We explore the issues in developing a basic semantic modeling framework for describing…
At its core, abstraction is the process of generalizing from specific instances to broader concepts or models, with the primary objective of reducing complexity while preserving properties essential to the intended purpose. It is…
The Special Affine Fourier Transformation or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Shift-invariant spaces also play an important role in…