On the Computational Power of Timed Differentiable Petri Nets
Haddad, Serge; Recalde, Laura; Silva, Manuel (2006), On the Computational Power of Timed Differentiable Petri Nets, dans Asarin, Eugene; Bouyer, Patricia, Formal Modeling and Analysis of Timed Systems 4th International Conference, FORMATS 2006, Paris, France, September 25-27, 2006, Proceedings, Springer : Berlin, p. 230-244. http://dx.doi.org/10.1007/11867340_17
TypeCommunication / Conférence
Titre du colloque4th International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS'06)
Date du colloque2006-09
Ville du colloqueParis
Pays du colloqueFrance
Titre de l'ouvrageFormal Modeling and Analysis of Timed Systems 4th International Conference, FORMATS 2006, Paris, France, September 25-27, 2006, Proceedings
Auteurs de l’ouvrageAsarin, Eugene; Bouyer, Patricia
Titre de la collectionLecture Notes in Computer Science
Numéro dans la collection4202
Nombre de pages369
MétadonnéesAfficher la notice complète
Résumé (EN)Well-known hierarchies discriminate between the computational power of discrete time and space dynamical systems. A contrario the situation is more confused for dynamical systems when time and space are continuous. A possible way to discriminate between these models is to state whether they can simulate Turing machine. For instance, it is known that continuous systems described by an ordinary differential equation (ODE) have this power. However, since the involved ODE is defined by overlapping local ODEs inside an infinite number of regions, this result has no significant application for differentiable models whose ODE is defined by an explicit representation. In this work, we considerably strengthen this result by showing that Time Differentiable Petri Nets (TDPN) can simulate Turing machines. Indeed the ODE ruling this model is expressed by an explicit linear expression enlarged with the “minimum” operator. More precisely, we present two simulations of a two counter machine by a TDPN in order to fulfill opposite requirements: robustness and boundedness. These simulations are performed by nets whose dimension of associated ODEs is constant. At last, we prove that marking coverability, submarking reachability and the existence of a steady-state are undecidable for TDPNs.
Mots-clésExpressiveness; Simulation; Coverability; Reachability; Steady-state Analysis; Time Differentiable Petri Nets (TDPN); dynamical systems
Affichage des éléments liés par titre et auteur.