Sebastian Mauser

Process mining based on regions of languages

In this paper we give an overview, how to apply region based methodsfor the synthesis of Petri nets from languages to process mining. The research domain of process mining aims at constructing a process modelfrom an event log, such that the process model can reproduce the log, and doesnot allow for much more behaviour than shown in the log. We here considerPetri nets to represent process models. Event logs can be interpreted as finite languages.Region based synthesis methods can be used to construct a Petri net froma language generating the minimal net behaviour including the given language.Therefore, it seems natural to apply such methods in the process mining domain.There are several different region based methods in literature yielding differentPetri nets. We adapt these methods to the process mining domain and comparethem concerning efficiency and usefulness of the resulting Petri net.

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.

Synthesis of Petri nets from infinite partial languages

In this paper we show an implementation of an algorithm to synthesize a place/transition Petri net (p/t-net) from a possibly infinite partial language, which is given by a term over a finite set of labelled partial orders (LPOs). The implementation is integrated as an extension of our Petri net toolset VipTool. The new extension comprises two plug-ins. The first plug-in offers editing features to specify term based partial languages. The specification of terms is graphically supported by a visualization similar to structograms as well as by a representation in the form of UML activity diagrams. The second new plug-in provides the algorithmic computation of a p/t-net synthesized from a term specification. This algorithm is in principle based on ideas already presented in the paper [4], but a so called separation computation is applied instead of the basis representation used in [4].

Construction of Process Models from Example Runs

This contribution suggests a novel approach for a systematic and automatic generation of process models from example runs. The language used for process models is place/transition Petri nets, the language used for example runs is labelled partial orders. The approach adopts techniques from Petri net synthesis and from process mining. In addition to a formal treatment of the approach, a case study is presented and implementation issues are discussed.

Synthesis of Petri Nets from Term Based Representations of Infinite Partial Languages

In this paper we present an algorithm to synthesize a finite unlabelled place/transition Petri net (p/t-net) from a possibly infinite partial language, which is given by a term over a finite set of labelled partial orders using operators for union, iteration, parallel composition and sequential composition. The synthesis algorithm is based on the theory of regions for partial languages presented in [17] and produces a p/t-net having minimal net behaviour including the given partial language. The algorithm uses linear programming techniques that were already successfully applied in [22] for the synthesis of p/t-nets from finite partial languages. Also, an equality test algorithm to check whether the behaviour of the synthesized p/t-net equals the given partial language is shown. Moreover, we present an implementation of the developed synthesis algorithm together with an example case study. Finally, a possible generalization of the presented term based representation of infinite partial languages is discussed.

Comparison of Different Algorithms to Synthesize a Petri Net from a Partial Language

In this paper we present two new algorithms that effectively synthesize a finite place/transition Petri net (p/t-net) from a finite set of labeled partial orders (a finite partial language). Either the synthesized p/t-net has exactly the non-sequential behavior specified by the partial language, or there is no such p/t-net. The first algorithm is an improved version of a synthesis algorithm presented in [14], which uses the classical theory of regions applied to the set of step sequences generated by the given partial language. Instead of computing all step sequences, the new algorithm directly works on appropriate prefixes specified in the partial language. The second algorithm is based on the theory of token flow regions for partial languages developed in [16,15,14]. While in [15,14] a so called basis representation is applied, the new algorithm combines the concepts of separation representation and token flows. We implemented both synthesis algorithms in our framework VipTool. A comparison of the two new algorithms with the two predecessor algorithms presented in [14,15]shows that both perform better than their respective predecessor. Therefore, a detailed comparison of these two synthesis algorithms is presented.

Modeling and mining of learnflows

This article transfers concepts and methods from business process modeling and workflow management to the field of learnflows, i.e. learning and teaching processes. It is first shown that these two areas have a lot of commonalities and similarities. On the other hand, there are also crucial specifics of learning processes that have to be taken into account additionally. We then introduce and discuss modeling languages for learnflows which are based on ideas from workflow modeling. Finally, we develop an approach to automatically generate learnflow models from log files of learning systems by adapting workflow mining methods.

Executability of scenarios in Petri nets

In this paper, we show that it can be tested in polynomial time as to whether a scenario is an execution of a Petri net. This holds for a wide variety of Petri net classes, ranging from elementary nets to general inhibitor nets. Scenarios are given by causal structures expressing causal dependencies and concurrency among events. In the case of elementary nets and of place/transition nets, such causal structures are partial orders among transition occurrences. For several extended Petri net classes, the extension of partial orders to stratified order structures is considered. The algorithms are based on the representation of the non-sequential behavior of Petri nets by so-called token flow functions and a characterization of Petri net executions called token flow property. This property allows nontrivial transformations into flow optimization problems, which can be solved in polynomial time. The paper is a revised, consolidated and extended version of the conference papers [G. Juhas, R. Lorenz, J. Desel, Can I execute my scenario in your net?, in: G. Ciardo, P. Darondeau (Eds.), ICATPN, in: Lecture Notes in Computer Science, Springer, 2005, pp. 289-308; R. Lorenz, S. Mauser, R. Bergenthum, Testing the Executability of Scenarios in General Inhibitor Nets, in: ACSD, IEEE Computer Society, 2007, pp. 167-176] and includes parts of the habilitation thesis [R. Lorenz, Szenario-basierte Verifikation und Synthese von Perinetzen: Theorie und Anwendungen, Habilitation, 2006].

Complete process semantics for inhibitor nets

In this paper we complete the semantical framework proposed in [13] for process and causality semantics of Petri nets by an additional aim and develop process and causality semantics of place/transition Petri nets with weighted inhibitor arcs (pti-nets) satisfying the semantical framework including this aim. The aim was firstly mentioned in [8] and states that causality semantics deduced from process nets should be complete w.r.t. step semantics in the sense that each causality structure which is consistent with the step semantics corresponds to some process net. We formulate this aim in terms of enabled causality structures. While it is well known that process semantics of place/transition Petri nets (p/t-nets) satisfy the additional aim, we show that the most general process semantics of pti-nets proposed so far [13] does not and develop our process semantics as an appropriate generalization.

Unfolding Semantics of Petri Nets Based on Token Flows

In this paper we propose two new unfolding semantics for general Petri nets combining the concept of prime event structures with the idea of token flows developed in [13]. In contrast to the standard unfolding based on branching processes, one of the presented unfolding models avoids to represent isomorphic processes while the other additionally reduces the number of (possibly nonisomorphic) processes with isomorphic underlying runs. We show that both the proposed unfolding models still represent the complete partial order behavior. Moreover, in both cases it is possible to construct complete finite prefixes for bounded nets through applying the known theory of cut-off events. In particular, canonical prefixes w.r.t. a given cutting context can be defined and computed for bounded nets. We present implementations of construction algorithms for complete finite prefixes of both the unfolding models. Experimental results show that the computed prefixes are much smaller and can be constructed significantly faster than in the case of the standard unfolding.