5,327 research outputs found
Learning Hybrid Process Models From Events: Process Discovery Without Faking Confidence
Process discovery techniques return process models that are either formal
(precisely describing the possible behaviors) or informal (merely a "picture"
not allowing for any form of formal reasoning). Formal models are able to
classify traces (i.e., sequences of events) as fitting or non-fitting. Most
process mining approaches described in the literature produce such models. This
is in stark contrast with the over 25 available commercial process mining tools
that only discover informal process models that remain deliberately vague on
the precise set of possible traces. There are two main reasons why vendors
resort to such models: scalability and simplicity. In this paper, we propose to
combine the best of both worlds: discovering hybrid process models that have
formal and informal elements. As a proof of concept we present a discovery
technique based on hybrid Petri nets. These models allow for formal reasoning,
but also reveal information that cannot be captured in mainstream formal
models. A novel discovery algorithm returning hybrid Petri nets has been
implemented in ProM and has been applied to several real-life event logs. The
results clearly demonstrate the advantages of remaining "vague" when there is
not enough "evidence" in the data or standard modeling constructs do not "fit".
Moreover, the approach is scalable enough to be incorporated in
industrial-strength process mining tools.Comment: 25 pages, 12 figure
Characterizing Behavioural Congruences for Petri Nets
We exploit a notion of interface for Petri nets in order to design a set of net combinators. For such a calculus of nets, we focus on the behavioural congruences arising from four simple notions of behaviour, viz., traces, maximal traces, step, and maximal step traces, and from the corresponding four notions of bisimulation, viz., weak and weak step bisimulation and their maximal versions. We characterize such congruences via universal contexts and via games, providing in such a way an understanding of their discerning powers
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
Socionic Multi-Agent Systems Based on Reflexive Petri Nets and Theories of Social Self-Organisation
This contribution summarises the core results of the transdisciplinary ASKO project, part of the German DFG's programme Sozionik, which combines sociologists' and computer scientists' skills in order to create improved theories and models of artificial societies. Our research group has (a) formulated a social theory, which is able to explain fundamental mechanisms of self-organisation in both natural and artificial societies, (b) modelled this in a mathematical way using a visual formalism, and (c) developed a novel multi-agent system architecture which is conceptually coherent, recursively structured (hence non-eclectic) and based on our social theory. The article presents an outline of both a sociological middle-range theory of social self-organisation in educational institutions, its formal, Petri net based model, including a simulation of one of its main mechanisms, and the multi-agent system architecture SONAR. It describes how the theory was created by a re-analysis of some grand social theories, by grounding it empirically, and finally how the theory was evaluated by modelling its concepts and statements.Multi-Agents Systems, Petri Nets, Self-Organisation, Social Theories
Scalable discovery of hybrid process models in a cloud computing environment
Process descriptions are used to create products and deliver services. To lead better processes and services, the first step
is to learn a process model. Process discovery is such a technique which can automatically extract process models from event logs.
Although various discovery techniques have been proposed, they focus on either constructing formal models which are very powerful
but complex, or creating informal models which are intuitive but lack semantics. In this work, we introduce a novel method that returns
hybrid process models to bridge this gap. Moreover, to cope with today’s big event logs, we propose an efficient method, called f-HMD,
aims at scalable hybrid model discovery in a cloud computing environment. We present the detailed implementation of our approach
over the Spark framework, and our experimental results demonstrate that the proposed method is efficient and scalabl
Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets
We analyze a timed Petri net model of an emergency call center which
processes calls with different levels of priority. The counter variables of the
Petri net represent the cumulated number of events as a function of time. We
show that these variables are determined by a piecewise linear dynamical
system. We also prove that computing the stationary regimes of the associated
fluid dynamics reduces to solving a polynomial system over a tropical
(min-plus) semifield of germs. This leads to explicit formul{\ae} expressing
the throughput of the fluid system as a piecewise linear function of the
resources, revealing the existence of different congestion phases. Numerical
experiments show that the analysis of the fluid dynamics yields a good
approximation of the real throughput.Comment: 21 pages, 4 figures. A shorter version can be found in the
proceedings of the conference FORMATS 201
Functorial Semantics for Petri Nets under the Individual Token Philosophy
Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of net
A Comparison of Petri Net Semantics under the Collective Token Philosophy
In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric (strict) monoidal categories. We use the notion of adjunction to express each connection. We also present a purely logical description of the collective token interpretation of net behaviours in terms of theories and theory morphisms in partial membership equational logic
Tightening the Complexity of Equivalence Problems for Commutative Grammars
We show that the language equivalence problem for regular and context-free
commutative grammars is coNEXP-complete. In addition, our lower bound
immediately yields further coNEXP-completeness results for equivalence problems
for communication-free Petri nets and reversal-bounded counter automata.
Moreover, we improve both lower and upper bounds for language equivalence for
exponent-sensitive commutative grammars.Comment: 21 page
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