Related papers: A logic for n-dimensional hierarchical refinement
Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model and analyze this combination of dynamics, ranging from mathematical descriptions,…
We define a general notion of transition system where states and action labels can be from arbitrary nominal sets, actions may bind names, and state predicates from an arbitrary logic define properties of states. A Hennessy-Milner logic for…
Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…
Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion.…
Covariant-contravariant simulation is a combination of standard (covariant) simulation, its contravariant counterpart and bisimulation. We have previously studied its logical characterization by means of the covariant-contravariant modal…
Deep Learning architectures, and in particular Transformers, are conventionally viewed as a composition of layers. These layers are actually often obtained as the sum of two contributions: a residual path that copies the input and the…
We describe here our perception of complex systems, of how we feel the different layers of description are important part of a correct complex system simulation. We describe a rough models categorization between rules based and law based,…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential…
Refinement calculus is a powerful and expressive tool for reasoning about sequential programs in a compositional manner. In this paper we present an extension of refinement calculus for reactive systems. Refinement calculus is based on…
Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these…
We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. We present several combinatorial characterisations of when the expressive power of this fragment coincides with that of the…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
Token representations in high-dimensional latent spaces often exhibit redundancy, limiting computational efficiency and reducing structural coherence across model layers. Hierarchical latent space folding introduces a structured…
Specification theories as a tool in model-driven development processes of component-based software systems have recently attracted a considerable attention. Current specification theories are however qualitative in nature, and therefore…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
Higher-dimensional automata (HDAs) are models of non-interleaving concurrency for analyzing concurrent systems. There is a rich literature that deals with bisimulations for concurrent systems, and some of them have been extended to HDAs.…
I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…