Gabriel Juhás

What Is a Petri Net? Informal Answers for the Informed Reader

The increasing number of Petri net variants naturally leads to the question whether the term “Petri net” is more than a common name for very different concepts. This contribution tries to identify aspects common to all or at least to most Petri nets. It concentrates on those features where Petri nets significantly differ from other modeling languages, i.e. we ask where the use of Petri nets leads to advantages compared to other languages. Different techniques that are usually comprised under the header “analysis” are distinguished with respect to the analysis aim. Finally, the role of Petri nets in the development of distributed systems is discussed.

Unifying Petri Nets

The increasing number of Petri net variants naturally leads to the question whether the term “Petri net” is more than a common name for very different concepts. This contribution tries to identify aspects common to all or at least to most Petri nets. It concentrates on those features where Petri nets significantly differ from other modeling languages, i.e. we ask where the use of Petri nets leads to advantages compared to other languages. Different techniques that are usually comprised under the header “analysis” are distinguished with respect to the analysis aim. Finally, the role of Petri nets in the development of distributed systems is discussed.

How to synthesize nets from languages: a survey

In this paper we present a survey on methods for the synthesis of Petri nets from behavioral descriptions given as languages. We consider place/transition Petri nets, elementary Petri nets and Petri nets with inhibitor arcs. For each net class we consider classical languages, step languages and partial languages as behavioral description. All methods are based on the notion of regions of languages. We identify two different types of regions and two different principles of computing from the set of regions of a language a finite Petri net generating this language. For finite or regular languages almost each combination of Petri net class, language type, region type and computation principle can be considered to compute such a net. Altogether, we present a framework for region-based synthesis of Petri nets from languages which integrates almost all known approaches and fills several remaining gaps in literature.

Modelling and validation with VipTool

This paper describes concepts and features of a new version of the VipTool. As for the original VipTool, the main issue of this software package is to generate, analyze and visualize process nets, representing the partial order behavior of business process models given by Petri nets. Whereas the original VipTool was implemented in the scripting language Python, the new VipTool is a completely new and modular implementation in Java that allows to add arbitrary extensions in a more flexible way. In this new version, several drawbacks that had appeared previously where eliminated. Moreover, the new VipTool contains additional features such as a more comfortable editor as well as eps- and XML-interfaces. The main improvement is a better support of stepwise validation of models and specifications and, alternatingly, partial verification (testing) of specification implementations. This paper also presents a small case study explaining how the VipTool supports these design steps.

Can i execute my scenario in your net

In this paper we present a polynomial algorithm to decide whether a scenario (given as a Labelled Partial Order) is executable in a given place/transition Petri net while preserving at least the given amount of concurrency (adding no causality). In the positive case the algorithm computes a process net that respects the concurrency formulated by the scenario. We moreover present a polynomial algorithm to decide whether the amount of concurrency given by a Labelled Partial Order is maximal, i.e. whether the Labelled Partial Order precisely matches a process net w.r.t. causality and concurrency of the events, if this process net represents a minimal causality of events among all process nets.

Towards synthesis of petri nets from scenarios

Given a set of scenarios, we answer the question whether this set equals the set of all executions of a Petri net. Formally, scenarios are expressed by (isomorphism classes of) labelled partial orders (LPOs), also known as pomsets or partial words. An LPO is an execution of a Petri net if it is a sequentialization of an LPO generated by a process of the net. We propose a definition of regions for a set of LPOs, i.e for a partial language. Given a partial language of scenarios, we prove a necessary and sufficient condition (based on regions) for the partial language of scenarios to be the partial language of executions of a place/transition Petri net. Finally, we prove our notion of regions to be consistent with the notion of regions of trace languages.

Petri Nets over Partial Algebra

Partial algebra is a suitable tool to define sequential semantics for arbitrary restrictions of the occurrence rule, such as capacity or context restrictions. This paper focuses on non-sequential process semantics of Petri nets over partial algebras. It is shown that the concept of partial algebra is suitable as a basis for process construction of different classes of Petri nets taking dependencies between processes that restrict concurrent composition into consideration.Thus, Petri nets over partial algebra provide a unifying framework for Petri net classes in which some processes cannot be executed concurrently, such as elementary nets with context. We will illustrate this claim proving a one-to-one correspondence between processes constructed using partial algebra and processes based on partial orders for elementary nets with context. Furthermore, we provide compositional process term semantics using the presented framework for place/transition nets with (both weak and strong) capacities and place/transition nets with inhibitor arcs.

Instance deadlock: a mystery behind frozen programs

In the paper we discuss the event-driven reactive programs and systems, which does not deadlock for one instance, but because of shared resources, can deadlock for several instances. We focus on event-driven programs, where instances have a correct finish, and resources can be used by single instances, but can neither be destroyed nor created by instances. Typical examples include workflow processes, where each case creates an instance of the process and instances share resources used to execute single activities. Formally, we model such event-driven programs and systems by workflow nets, enriched by so called static places, introduced in [3] as resource constrained workflow nets (rcwf-nets). We investigate, whether an rcwf-net, which is sound for a single instance is sound for multiple instances (dynamically sound) or whether it contains an instance deadlock for a number of instances. We show that the detection of instance deadlock and the dynamic soundness of rcwf-nets is decidable by transforming the problem to bounded place/transition Petri nets.

Can i execute my scenario in your net? viptool tells you!

This paper describes the verification module (the VipVerify Module) of the VipTool [4]. VipVerify allows to verify whether a given scenario is an execution of a system model, given by a Petri net. Scenarios can be graphically specified by means of Labeled Partial Orders (LPOs). A specified LPO is an execution of a Petri net if it is a (partial) sequentialization of an LPO generated by a process of the net. We have shown in [2] that the executability of an LPO can be tested by a polynomial algorithm. The VipVerify Module implements this algorithm. If the test is positive, the corresponding process is computed and visualized. If the test is negative, a maximal executable prefix of the LPO is computed and visualized, together with a corresponding process and the set of those following events in the LPO which are not enabled to occur after the occurrence of the prefix. Further, the VipVerify Module allows to test in polynomial time whether a scenario equals an execution with minimal causality. A small case study illustrates the verification of scenarios w.r.t. business process models.

Finite Unfoldings of Unbounded Petri Nets

The aim of this paper is to introduce a concept for an efficient representation of the behavior of an unbounded Petri net. This concept combines a known method for the description of unbounded Petri nets, namely coverability trees, with an efficient, partial order based method developed for bounded Petri nets, namely Petri net unfoldings.