Nets, time and space

State space computation and analysis of Time Petri Nets

The theory of Petri Nets provides a general framework to specify the behaviors of real-time reactive systems and Time Petri Nets were introduced to take also temporal specifications into account. We present in this paper a forward zone-based algorithm to compute the state space of a bounded Time Petri Net: the method is different and more efficient than the classical State Class Graph. We prove...

Time Petri Nets State Space Reduction Using Dynamic Programming

In this paper a parametric description for the state space of an arbitrary TPN is given. An enumerative procedure for reducing the state space is introduced. The reduction is defined as a truncated multistage decision problem and solved recursively. A reachability graph is defined in a discrete way by using the reachable integer-states of the TPN.

Eecient State Space Search for Time Petri Nets

Partial-order reduction methods provide a number of well studied methods that have been succesfully applied to the state-space explosion problem that arises when analysing state based models of concurrent and reactive systems. The techniques have mainly been studied within the context of untimed systems, in the context of real-time systems little progress has been made. The main problem seems t...

Efficient State Space Search for Time Petri Nets

Lipschitz maps and nets in Euclidean space

for x 6= x′. A set Y ⊂ Rn is a net if there is an R such that d(x, Y ) < R for every x ∈ Rn; it is separated if there is an ǫ > 0 such that |y − y′| > ǫ > 0 for every pair y 6= y′ in Y . History. In 1965, J. Moser showed that any two positive, C∞ volume forms on a compact manifold with the same total mass are related by a diffeomorphism [Mos]. Extensions of this result to other smoothness class...