Abstract
Timed-Arcs Petri nets (TaPN-nets) are a time extension of Petri nets that allows assigning clocks to tokens. System of dynamic points on a metric graph (DP-systems) is another dynamical model that is studied in discrete geometry dynamics and motivated by study of localized Gaussian wave packets scattering on thin structures; as well, DP-systems could be utilized to overapproximate the dynamics of messages scattering in distributed systems. In the latter case, time-temporal properties of DP-systems become a matter of interest. However, there are no tools that enable us to analyse them. In this work, we provide a new approach to automated analysis of DP-systems using the translation of a DP-system into a TaPN-net which is implemented as a TAPAAL plugin. The translation let us use the comprehensive tool support for TaPN-nets (TAPAAL/UPPAAL) to analyze DP-systems dynamical characteristics expressed in TCTL language. We demonstrated how to express some of them and verify time-temporal properties of a DP-system using the suggested approach, and performed experiments to obtain empirical estimates of the tool performance.
Highlights
The notion of a Petri nets evolved from a chemistry process model to a model of indefinitely expandable computing system consistent with laws of physics in C.A
System of dynamic points on a metric graph (DP-systems) is another dynamical model that is studied in discrete geometry dynamics and motivated by study of localized Gaussian wave packets scattering on thin structures; as well, DP-systems could be utilized to overapproximate the dynamics of messages scattering in distributed systems
A dynamical system consisting of a metric graph and dynamic points moving along the graph edges (DP-system) is a geometrical discrete dynamical system originally motivated by the problem of evolution of wave packets in thin structures
Summary
The notion of a Petri nets evolved from a chemistry process model to a model of indefinitely expandable computing system consistent with laws of physics in C.A. Points in a DPsystem may represent supports of Gaussian wave packets in a quantum graph and/or the projection of wave propagation on medium geodesics Both models, Petri nets and DP-systems, embrace realtime dynamics of discrete entities moving within a topological structure defined by a graph. A time semantics with restricted urgency was recently suggested for TaPN-nets in [24]; the suggested semantics allows urgent transitions to consume tokens only from the bounded places of a Petri net, and this restriction makes some behavioural problems decidable for TaPN-nets. In [26], timed-arc Petri nets were consistently combined with ‘nets-within-nets’ hierarchical structure and sound time semantics was provided; the decidability of behavioural coverabilityrelated properties using the notion of well-structured transition systems was established. A time elapsing step is allowed if there are no ′ ∈ [0, ) such that the + ′ marking has urgent transitions
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