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, in 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
Conference title4th International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS'06)
Book titleFormal Modeling and Analysis of Timed Systems 4th International Conference, FORMATS 2006, Paris, France, September 25-27, 2006, Proceedings
Book authorAsarin, Eugene; Bouyer, Patricia
Series titleLecture Notes in Computer Science
Number of pages369
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Abstract (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.
Subjects / KeywordsExpressiveness; Simulation; Coverability; Reachability; Steady-state Analysis; Time Differentiable Petri Nets (TDPN); dynamical systems
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