Homological properties of non-deterministic branchings of mergings in higher dimensional automata.
Homotopical interpretation of globular complex by multipointed d-space.
Integral nets and fuzzy relations in deterministic automata
Inverting weak dihomotopy equivalence using homotopy continuous flow.
Les symétries dans les réseaux de Petri stochastiques (RdPS). Construction du graphe symbolique
Les Symétries dans les Réseaux de Petri Stochastiques (RdPS) Construction du Graphe Symbolique
The main purpose of this paper is to give a method for construction of the reduced reachability graph for Stochastic Petri Nets (SPN), the symbolic graph. This construction is achieved by exploiting the structural symetries in the net using the theory of bisimulation of places for detecting isomorphic parts in the net. The symbolic graph, being isomorphic to an agregated Markov chain, may be used to prove qualitative properties as liveness, boundness, ... Moreover, this reduced graph make more...
Lower and upper bounds of shortest paths in reachability graphs.
Modeling shortest path games with Petri nets: a Lyapunov based theory
In this paper we introduce a new modeling paradigm for shortest path games representation with Petri nets. Whereas previous works have restricted attention to tracking the net using Bellman's equation as a utility function, this work uses a Lyapunov-like function. In this sense, we change the traditional cost function by a trajectory-tracking function which is also an optimal cost-to-target function. This makes a significant difference in the conceptualization of the problem domain, allowing the...
Modelling integer linear programs with Petri nets
Modelling integer linear programs with petri nets*
We show in this paper that timed Petri nets, with one resource shared by all the transitions, are directly connected to the modelling of integer linear programs (ILP). To an ILP can be automatically associated an equivalent Petri net. The optimal reachability delay is an optimal solution of the ILP. We show next that a net can model any ILP. I order to do this, we give a new sufficient reachability condition for the marking equation, which also holds for general Petri nets without timed transitions. ...
Normalization of place/transition-systems preserves net behaviour
On a computational approach to multiple contacts / impacts of elastic bodies
The analysis of dynamic contacts/impacts of several deformable bodies belongs to both theoretically and computationally complicated problems, because of the presence of unpleasant nonlinearities and of the need of effective contact detection. This paper sketches how such difficulties can be overcome, at least for a model problem with several elastic bodies, using i) the explicit time-discretization scheme and ii) the finite element technique adopted to contact evaluations together with iii) the...
On coalgebras and type transformations
We show that for an arbitrary Set-endofunctor T the generalized membership function given by a sub-cartesian transformation μ from T to the filter functor 𝔽 can be alternatively defined by the collection of subcoalgebras of constant T-coalgebras. Sub-natural transformations ε between any two functors S and T are shown to be sub-cartesian if and only if they respect μ. The class of T-coalgebras whose structure map factors through ε is shown to be a covariety if ε is a natural and sub-cartesian mono-transformation....
On -fuzzy Petri nets.
On the analysis of Petri nets and their synthesis from process languages
Processes in Place/Transition (P/T) nets are defined inductively by a peculiar numbering of place occurrences. Along with an associative sequential composition called catenation and a neutral process, a monoid of processes is obtained. The power algebra of this monoid contains all process languages with appropriate operations on them. Hence the problems of analysis and synthesis, analogous to those in the formal languages and automata theory, arise. Here, the analysis problem is: for a given P/T...
On the Analysis of Petri Nets and their Synthesis from Process Languages
Processes in Place/Transition (P/T) nets are defined inductively by a peculiar numbering of place occurrences. Along with an associative sequential composition called catenation and a neutral process, a monoid of processes is obtained. The power algebra of this monoid contains all process languages with appropriate operations on them. Hence the problems of analysis and synthesis, analogous to those in the formal languages and automata theory, arise. Here, the analysis problem is: for a given P/T...
On the hierarchy of Petri net languages
On the homology of small categories and asynchronous transition systems.
On the structure of recognizable languages of dependence graphs
Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency.