Related papers: On the homology language of HDA models of transiti…
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…
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…
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…
We introduce weak morphisms of higher dimensional automata and use them to define preorder relations for HDAs, among which homeomorphic abstraction and trace equivalent abstraction. It is shown that homeomorphic abstraction is essentially…
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…
This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between…
The synchronization problem is investigated for the class of locally strongly transitive automata introduced in a previous work of the authors. Some extensions of this problem related to the notions of stable set and word of minimal rank of…
The purpose of this paper is to provide a construction to model shared-variable systems using higher-dimensional automata which is compositional in the sense that the parallel composition of completely independent systems is modeled by the…
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…
Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie…
This paper presents and analyzes an incremental algorithm for the construction of Acyclic Non-deterministic Finite-state Automata (NFA). Automata of this type are quite useful in computational linguistics, especially for storing lexicons.…
We report some further developments regarding the language theory of higher-dimensional automata (HDAs). Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) with interfaces. We show a pumping lemma…
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…
Hybrid systems are dynamical systems with continuous evolution of states and discrete evolution of states and governing equations. We have worked on the design and implementation of HydLa, a constraint-based modeling language for hybrid…
We introduce a notion of synchronization for higher-dimensional automata, based on coskeletons of cubical sets. Categorification transports this notion to the setting of categorical transition systems. We apply the results to study the…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
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…
Higher dimensional automata (HDAs) provide a geometric model of true concurrency, yet their standard formulation encodes an artificial total order on events. This representational artifact causes a fundamental mismatch between the…
We show that a set with an action of a locally finite-dimensional free partially commutative monoid and the corresponding semicubical set have isomorpic homology groups. We build a complex of finite length for the computing homology groups…