Timed and Stochastic Model Checking of Petri Nets

2012

Petri nets are graphical and mathematical modeling tools which are gaining popularity in recent years. It is a tool for the representation of complex logical systems, such as synchronization, sequentially, concurrency and conflict. The present introduction highlights some of the formalism of Petri nets with special emphasis on reachability and coverability analysis. We have also extended our topic by explaining place & transition invariance with examples.

Journal of Computational Methods in Sciences and Engineering, 2005

PN (PN) are tools for the analysis and design of concurrent systems. There is a formal theory, which supports PN. An extension of PN is Petri Nets with Clocks (PNwC). PNwC are useful to model systems with temporal requirements via specification of clocks, using temporal invariants for the places and temporal conditions in the transitions. Using invariants in places allows the specifications of hard deadlines constrains (upper bound constrains): when a deadline is reached the progress of time is blocked by the invariant and the action becomes urgent. An algorithm for the analysis of a PNwC has been proposed in [1]. The algorithm is oriented to the verification and correction of errors in the modelling of the time variable. The algorithm generates information about temporal unreachable states and process deadlocks with temporal blocks. Also, it corrects places invariants and transitions conditions. We present here a formalism for PNwC based on Timed Graphs. The analysis algorithm is presented here using the formalism. We show here how Petri Net theory can be joined with Timed Graph theory to construct a formalism, which supports a tool for the analysis of models of concurrent process with real time specification.

2009

The Petri net formalism has been used to model many types of systems, in particular, concurrent, distributed and non-deterministic. Important system properties, such as liveness and safety, can be studied based on the system's net model. A means of analysing its behaviour is by examining its net structure.

Journal of Computers, 2009

In this paper, we propose to study and analyze the tasks of a robot and the interaction with its environment, by using the power of Petri nets modelling, especially the timed nets. Our system consists of a robot, a programmable automaton and a computer. We consider the execution of the tasks taking into account the temporal constraints. So, we use the temporal Petri nets to model the whole system and also for its verification. We describe the obtained Petri net and the constraints textually or graphically in the environment TINA, an open source tool dedicated for timed Petri nets. We note that the Petri nets have good qualities of abstraction from the modelling point of view compared to the finite state machines which suffer from the states explosion problem, related to the accessibility graph. Moreover, the consideration of the temporal constraints adds an important complexity to the problem; the system which was carried out successfully in the case "without temporal constraints", can get in a dead lock state in the case "with temporal constraints" if these constraints are not satisfied.

IEEE Transactions on Industrial Informatics, 2000

2000

IEEE Transactions on Software Engineering, 1991

Petri nets are a powerful formalism for the specification and analysis of concurrent systems. Thanks to their flexibility, they have been extended and modified in several ways in order to match the requirements of specific application areas. In particular, since Petri nets easily model control flow, some extensions have been proposed to deal with functional aspects while others have taken timing issues into account. Unfortunately, so far little has been done to integrate these aspects, that are crucial in the case of time-critical systems. In this paper, we introduce a high-level Petri net formalism (ER nets) which can be used to specify control, function, and timing issues. In particular, we discuss how time can be modeled via ER nets by providing a suitable axiomatization. Then, we use ER nets to define a time notation (called TB nets), which is shown to generalize most time Petri net-based formalisms which appeared in the literature. Finally, we discuss how ER nets can be used in a specification support environment for time critical system and, in particular, the kind of analysis supported.

1996

2001