On the Computational Power of Timed Differentiable Petri Nets

Abstract. 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 count...

• Type: Conference
• Year: 2006
• Where: FORMATS
• Authors: Serge Haddad, Laura Recalde, Manuel Silva
• Keywords: Dynamical Systems, Formal Methods, FORMATS 2006, Space Dynamical Systems, Turing Machines