Related papers: Abstractions of Sequences, Functions and Operators

Program slicing provides explanations that illustrate how program outputs were produced from inputs. We build on an approach introduced in prior work by Perera et al., where dynamic slicing was defined for pure higher-order functional…

We present a Galois theory connecting finitary operations with pairs of finitary relations one of which is contained in the other. The Galois closed sets on both sides are characterised as locally closed subuniverses of the full iterative…

We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…

This study introduces a procedure to obtain general expressions, $y = f(x)$, subject to linear constraints on the function and its derivatives defined at specified values. These constrained expressions can be used describe functions with…

Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…

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…

Inspired by recent strides in empirical efficacy of implicit learning in many robotics tasks, we seek to understand the theoretical benefits of implicit formulations in the face of nearly discontinuous functions, common characteristics for…

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…

Functional coroutines are a restricted form of control mechanism, where each coroutine is represented with both a continuation and an environment. This restriction was originally obtained by considering a constructive version of Parigot's…

Translating continuous control system models into finite automata allows us to use powerful discrete tools to synthesize controllers for complex specifications. The abstraction construction step is unfortunately hamstrung by high runtime…

Iterative abstraction refinement techniques are one of the most prominent paradigms for the analysis and verification of systems with large or infinite state spaces. This paper investigates the changes of truth values of system properties…

We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…

We develop a general framework for agent abstraction based on the situation calculus and the ConGolog agent programming language. We assume that we have a high-level specification and a low-level specification of the agent, both represented…

Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured…

In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines…

The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.

We describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines for higher-order and imperative programming languages. To…

Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers.…

Generalized planning is about finding plans that solve collections of planning instances, often infinite collections, rather than single instances. Recently it has been shown how to reduce the planning problem for generalized planning to…

We design an abstract setting for the approximation in Banach spaces of operators acting in duality. A typical example are the gradient and divergence operators in Lebesgue--Sobolev spaces on a bounded domain. We apply this abstract setting…