Mining structured Petri nets for the visualization of process behavior

Visualization is essential for understanding the models obtained by process mining. Clear and efficient visual representations make the embedded information more accessible and analyzable. This work presents a novel approach for generating process models with structural properties that induce visually friendly layouts. Rather than generating a single model that captures all behaviors, a set of Petri net models is delivered, each one covering a subset of traces of the log. The models are mined by extracting slices of labelled transition systems with specific properties from the complete state space produced by the process logs. In most cases, few Petri nets are sufficient to cover a significant part of the behavior produced by the log.Peer ReviewedPostprint (author's final draft

Effective representation of RT-LOTOS terms by finite time petri nets

The paper describes a transformational approach for the specification and formal verification of concurrent and real-time systems. At upper level, one system is specified using the timed process algebra RT-LOTOS. The output of the proposed transformation is a Time Petri net (TPN). The paper particularly shows how a TPN can be automatically constructed from an RT-LOTOS specification using a compositionally defined mapping. The proof of the translation consistency is sketched in the paper and developed in [1]. The RT-LOTOS to TPN translation patterns formalized in the paper are being implemented. in a prototype tool. This enables reusing TPNs verification techniques and tools for the profit of RT-LOTOS

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

On Fault Diagnosis of random Free-choice Petri Nets

This paper presents an on-line diagnosis algorithm for Petri nets where a priori probabilistic knowledge about the plant operation is available. We follow the method developed by Benveniste, Fabre, and Haar to assign probabilities to configurations in a net unfolding thus avoiding the need for randomizing all concurrent interleavings of transitions. We consider different settings of the diagnosis problem, including estimating the likelihood that a fault may have happened prior to the most recent observed event, the likelihood that a fault will have happened prior to the next observed event. A novel problem formulation treated in this paper considers deterministic diagnosis of faults that occurred prior to the most recent observed event, and simultaneous calculation of the likelihood that a fault will occur prior to the next observed event

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