Related papers: Weak morphisms of higher dimensional automata
This paper introduces a notion of equivalence for higher-dimensional automata, called weak equivalence. Weak equivalence focuses mainly on a traditional trace language and a new homology language, which captures the overall independence…
Higher dimensional automata, i.e. labelled precubical sets, model concurrent systems. We introduce the homology graph of an HDA, which is a directed graph whose nodes are the homology classes of the HDA. We show that the homology graph is…
Higher-dimensional automata constitute a very expressive model for concurrent systems. In this paper, we discuss "topological abstraction" of higher-dimensional automata, i.e., the replacement of HDAs by smaller ones that can be considered…
The theory of higher-dimensional automata (HDAs) has seen rapid progress in recent years, and first applications, notably to Petri net analysis, are starting to show. It has, however, emerged that HDAs themselves often are too strict a…
We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event…
It is shown that a higher-dimensional automaton is hhp-bisimilar to the free symmetric HDA generated by it. Consequently, up to hereditary history-preserving bisimilarity, ordinary HDAs and symmetric HDAs are models of concurrency with the…
Higher-dimensional automata (HDA) are a model of concurrency that models simultaneous execution of events using higher dimensional cells. HDA recognize languages of pomsets, a generalization of finite words whose letters are partially…
Given a transition system with an independence relation on the alphabet of labels, one can associate with it a usually very large symmetric higher-dimensional automaton. The purpose of this paper is to show that by choosing an acyclic…
We formalize the semantics of hybrid systems as sets of hybrid trajectories, including those generated by an hybrid transition system. We study the abstraction of hybrid trajectory semantics for verification, static analysis, and…
We construct labeling homomorphisms on the cubical homology of higher-dimensional automata and show that they are natural with respect to cubical dimaps and compatible with the tensor product of HDAs. We also indicate two possible…
The strength of a dynamic language is also its weakness: run-time flexibility comes at the cost of compile-time predictability. Many of the hallmarks of dynamic languages such as closures, continuations, various forms of reflection, and a…
Higher-dimensional automata (HDA) are a formalism to faithfully model the behaviour of concurrent systems. For ordinary automata, there is a correspondence between regular expressions, regular languages and finite automata, which provides a…
In this paper we study finite higher-dimensional automata (HDAs) from the logical point of view. Languages of HDAs are sets of finite bounded-width interval pomsets with interfaces (iiPoms<=k) closed under order extension. We prove that…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
We describe a construction that to each algebraically specified notion of higher-dimensional category associates a notion of homomorphism which preserves the categorical structure only up to weakly invertible higher cells. The construction…
We characterise the problem of abstraction in the context of deep reinforcement learning. Various well established approaches to analogical reasoning and associative memory might be brought to bear on this issue, but they present…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
We introduce a new category of higher-dimensional automata in which the morphisms are functional homotopy simulations, i.e. functional simulations up to concurrency of independent events. For this, we use unfoldings of higher-dimensional…
We introduce higher-dimensional automata for infinite interval ipomsets ($\omega$-HDAs). We define key concepts from different points of view, inspired from their finite counterparts. Then we explore languages recognized by $\omega$-HDAs…
Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of omega-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is…