Goal-Driven Unfolding of Petri Nets

Unfoldings provide an efficient way to avoid the state-space explosion due to interleavings of concurrent transitions when exploring the runs of a Petri net. The theory of adequate orders allows one to define finite prefixes of unfoldings which contain all the reachable markings. In this paper we are interested in reachability of a single given marking, called the goal. We propose an algorithm for computing a finite prefix of the unfolding of a 1-safe Petri net that preserves all minimal configurations reaching this goal. Our algorithm combines the unfolding technique with on-the-fly model reduction by static analysis aiming at avoiding the exploration of branches which are not needed for reaching the goal. We present some experimental results

Back in Time Petri Nets

11th Int. Conf. on Formal Modeling and Analysis of Timed Systems (FORMATS'13) July 2013 Buenos AiresInternational audienceThe time progress assumption is at the core of the semantics of real-time formalisms. It is also the major obstacle to the development of partial-order techniques for real-time distributed systems since the events are ordered both by causality and by their occurrence in time. Anyway, extended free choice safe time Petri nets (TPNs) were already identi ed as a class where partial order semantics behaves well. We show that, for this class, the time progress assumption can even be dropped (time may go back in case of concurrency), which establishes a nice relation between partial-order semantics and time progress assumption

Timed Alignments with Mixed Moves

The subject of this paper is to study conformance checking for timed models, that is, process models that consider both the sequence of events in a process as well as the timestamps at which each event is recorded. Time-aware process mining is a growing subfield of research, and as tools that seek to discover timing related properties in processes develop, so does the need for conformance checking techniques that can tackle time constraints and provide insightful quality measures for time-aware process models. In particular, one of the most useful conformance artefacts is the alignment, that is, finding the minimal changes necessary to correct a new observation to conform to a process model. This paper follows a previous one, where we have set our problem of timed alignment. In the present paper, we solve the case where the metrics used to compare timed processes allows mixed moves, i.e. an error on the timestamp of an event may or may not have propagated to its successors, and provide linear time algorithms for distance computation and alignment on models with sequential causal processes.Comment: arXiv admin note: text overlap with arXiv:2207.0187

An A*-algorithm for computing discounted anti-alignments in process mining

Process mining techniques aim at analyzing and monitoring processes through event data. Formal models like Petri nets serve as an effective representation of the processes. A central question in the field is to assess the conformance of a process model with respect to the real process executions. The notion of anti-alignment, which represents a model run that is as distant as possible to the process executions, has been demonstrated to be crucial to measure precision of models. However, the only known algorithm for computing anti-alignments has a high complexity, which prevents it from being applied on real-life problem instances. In this paper we propose a novel algorithm for computing anti-alignments, based on the well-known graph-based A* scheme. By introducing a discount factor in the edit distance used for the search of anti-alignments, we obtain the first efficient algorithm to approximate them. We show how this approximation is quite accurate in practice, by comparing it with the optimal results for small instances where the optimal algorithm can also compute anti-alignments. Finally, we compare the obtained precision metric with respect to the state-of-the-art metrics in the literature for real-life examples.Peer ReviewedPostprint (author's final draft

Alignment-based trace clustering

A novel method to cluster event log traces is presented in this paper. In contrast to the approaches in the literature, the clustering approach of this paper assumes an additional input: a process model that describes the current process. The core idea of the algorithm is to use model traces as centroids of the clusters detected, computed from a generalization of the notion of alignment. This way, model explanations of observed behavior are the driving force to compute the clusters, instead of current model agnostic approaches, e.g., which group log traces merely on their vector-space similarity. We believe alignment-based trace clustering provides results more useful for stakeholders. Moreover, in case of log incompleteness, noisy logs or concept drift, they can be more robust for dealing with highly deviating traces. The technique of this paper can be combined with any clustering technique to provide model explanations to the clusters computed. The proposed technique relies on encoding the individual alignment problems into the (pseudo-)Boolean domain, and has been implemented in our tool DarkSider that uses an open-source solver.Peer ReviewedPostprint (author's final draft

Timed Alignments with Mixed Moves

The subject of this paper is to study conformance checking for timed models, that is, process models that consider both the sequence of events in a process as well as the timestamps at which each event is recorded. Time-aware process mining is a growing subfield of research, and as tools that seek to discover timing related properties in processes develop, so does the need for conformance checking techniques that can tackle time constraints and provide insightful quality measures for time-aware process models. In particular, one of the most useful conformance artefacts is the alignment, that is, finding the minimal changes necessary to correct a new observation to conform to a process model. This paper follows a previous one, where we have set our problem of timed alignment. In the present paper, we solve the case where the metrics used to compare timed processes allows mixed moves, i.e. an error on the timestamp of an event may or may not have propagated to its successors, and provide linear time algorithms for distance computation and alignment on models with sequential causal processes

Goal-Driven Unfolding of Petri Nets

International audienceUnfoldings provide an efficient way to avoid the state-space explosion due to interleavings of concurrent transitions when exploring the runs of a Petri net. The theory of adequate orders allows one to define finite prefixes of unfoldings which contain all the reachable markings. In this paper we are interested in reachability of a single given marking, called the goal. We propose an algorithm for computing a finite prefix of the unfolding of a 1-safe Petri net that preserves all minimal configurations reaching this goal. Our algorithm combines the unfolding technique with on-the-fly model reduction by static analysis aiming at avoiding the exploration of branches which are not needed for reaching the goal. We present some experimental results

Goal-Driven Unfolding of Petri Nets

International audienceUnfoldings provide an efficient way to avoid the state-space explosion due to interleavings of concurrent transitions when exploring the runs of a Petri net. The theory of adequate orders allows one to define finite prefixes of unfoldings which contain all the reachable markings. In this paper we are interested in reachability of a single given marking, called the goal. We propose an algorithm for computing a finite prefix of the unfolding of a 1-safe Petri net that preserves all minimal configurations reaching this goal. Our algorithm combines the unfolding technique with on-the-fly model reduction by static analysis aiming at avoiding the exploration of branches which are not needed for reaching the goal. We present some experimental results