Formalization of petri nets with clocks

2020

Copy right Idea Grou p Inc. Copy right Idea Grou p Inc. ABSTRACT Petri Nets are tools for the analysis and design of concurrent systems. There is a formal theory, which supports Petri Nets. We propose Petri Nets with Clocks (PNwC) which has a high expressive power in the concurrent and asynchronous process modeling and gives the possibility to model real time systems. The Petri Nets with Clocks are useful to model systems with temporal requirements via specification of clocks, using temporal invariants for the places and temporal conditions in the transitions. In PNwC we force to specifies invariants in places and 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], [2]. This algorithm is oriented to the verification and correction of errors in t...

Theoretical Computer Science, 1998

We define formally the notion of implementation for time critical systems in terms of provability of properties described abstractly at the specification level. We characterize this notion in terms of formulas of the temporal logic TRIO and operational models of timed Petri nets, and provide a method to prove that two given nets are in the implementation relation. Refinement steps are often used as a means to derive in a systematic way the system design starting from its abstract specification. We present a method to formally prove the correctness of refinement rules for timed Petri nets and apply it to a few simple cases. We show how the possibility to retain properties of the specification in its implementation can simplify the verification of the designed systems by performing incremental analysis at various levels of the specification/implementation hierarchy.

ACM SIGSOFT Software Engineering Notes, 1989

Petri nets have been widely used in the past to model vari&s types of concurrent systems, including real-time systems. To do so, a variety of ad-hoc solutions have been proposed in order to allow time to be taken into account in specifications. In this paper, we initially survey these proposals and then we illustrate a new proposal (TEI nets), that unifies and generalizes all pre,vious ones. Next, we discuss how these and possibly other enrichments of the original model can be formally defined. This will be do,ne in terms of a high-level net model, called ER nets. The ability of ER nets to express a variety of behaviors justifies our choice to use them as a kernel formalism of a specification support environment that we are currently developing. In this environment, it will be possible to define new graphical notations for formal specifications and give them formal semantics in terms of the underlying ER model. This allows the specifier to tune the notation used in formal specifications to the particular expressive needs arising while modelling an application and yet base the notation on firm and rigorous grounds.

Third IEEE International Conference on Software Engineering and Formal Methods (SEFM'05), 2005

Petri nets are a graph-based modelling formalism which has been widely used for the formal specification and analysis of concurrent systems. A common analysis technique is that of state space exploration (or reachability analysis). Here, every possible reachable state of the system is generated and desirable properties are evaluated for each state. This approach has the great advantage of conceptual simplicity, but the great disadvantage of being susceptible to state space explosion, where the number of states is simply too large for exhaustive exploration. Many reduction techniques have been suggested to ameliorate the problem of state space explosion. In the case of timed systems, the state space is infinite, unless analysis is restricted to a bounded time period. In this paper, we present a Petri net formalism based on the notion of relative time (as opposed to the traditional approach of dealing with absolute time). The goal is to derive a finite state space for timed systems which have repeating patterns of behaviour, even though time continues to advance indefinitely.

2010 17th International Symposium on Temporal Representation and Reasoning, 2010

Real-time distributed systems may be modeled in different formalisms such as time Petri nets (TPN) and networks of timed automata (NTA). This paper focuses on translating a 1-bounded TPN into an NTA and considers an equivalence which takes the distribution of actions into account. This translation is extensible to bounded TPNs. We first use S-invariants to decompose the net into components that give the structure of the automata, then we add clocks to provide the timing information. Although we have to use an extended syntax in the timed automata, this is a novel approach since the other transformations and comparisons of these models did not consider the preservation of concurrency.

2018

The modeling and performance analysis of concurrent systems using Petri nets is considered under a useful timing model: probabilistic (i.e. exponential) delay distributions. While the focus is on decisionfree concurrent systems, i.e. marked graphs (MG), generalizations are identified to allow limited choice. A tight state space is efficiently constructed, through hierarchical decomposition followed by composition, which defines the time evolution of the system. Efficient algorithmic solution techniques and tools are also presented. Interesting analogies to biological and physical systems are highlighted.

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.

Lecture Notes in Computer Science, 2001

We set the ground for research on a timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. The novelty is that, rather than a single global clock, we use a set of unrelated clocks-possibly one per place-allowing a local timing as well as distributed time synchronisation. We give a formal definition of the model and investigate properties of local versus global timing, including decidability issues and notions of processes of the respective models.

The International Journal of Advanced Manufacturing Technology, 2008

Timed PNs enhance modelling capability of PNs by modifying the basic PN semantics to model temporal relations and constraints of a system. This modification makes their analysis more difficult. For example, the existing techniques for reachability analysis of Time PNs is not well suited for dealing with the end-to-end timing issues, and PN based scheduling makes it difficult to use criteria other than makespan, e.g., tardiness. This paper proposes a class of PNs to model time that improves the current analysis techniques and overcomes these difficulties. Temporal constraints are modelled through arc weights that determine the enabling and firing of transitions to generate its reachability tree used for behavioural analysis as in PNs. All transitions fire instantaneously. Time is represented as a state of the system.

2001

Petri Nets are tools for the analysis and design of concurrent systems. There is a formal theory, which supports Petri Nets. We propose Petri Nets with Clocks which has a high expressive power in the concurrent and asynchronous process modeling and gives the possibility to model real time systems. The Petri Nets with Clocks are useful to model systems with temporal requirements via specification of clocks, using temporal invariants for the places and temporal conditions in the transitions. Also, we have developed an algorithm for the analysis of Petri Nets with Clocks. For the Business Processes Modeling, we propose to use Petri Nets with Clocks to formalize models, allowing to study the models through a quantitative and qualitative analysis. Petri Nets with Clocks includes additional temporal elements-clocks-, which are appropriate for the Business Processes Modeling and are not taken into consideration in the literature concerning the extensions of Petri Nets with time. Petri Nets with Clocks allows studying the structural properties of Business Processes Modeling. This study not only allows the simulation but also verifies formally the model. It is oriented to the verification and correction of errors in the modeling of the time variable en Business Processes.