Theoretical Computer Science
Analog computation via neural networks
Theoretical Computer Science
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
Universal computation and other capabilities of hybrid and continuous dynamical systems
Theoretical Computer Science - Special issue on hybrid systems
What's decidable about hybrid automata?
Journal of Computer and System Sciences
Achilles and the tortoise climbing up the arithmetical hierarchy
Journal of Computer and System Sciences - Fourteenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
Decidability results in First–Order Hybrid PetriNets
Discrete Event Dynamic Systems
Formal languages and their relation to automata
Formal languages and their relation to automata
Discrete, Continuous, and Hybrid Petri Nets
Discrete, Continuous, and Hybrid Petri Nets
Refining the undecidability frontier of hybrid automata
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Petri nets and integrality relaxations: A view of continuous Petri net models
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Continuous Petri nets: expressive power and decidability issues
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
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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.