422 research outputs found
A recursive paradigm for aligning observed behavior of large structured process models
The alignment of observed and modeled behavior is a crucial problem in process mining, since it opens the door for conformance checking and enhancement of process models. The state of the art techniques for the computation of alignments rely on a full exploration of the combination of the model state space and the observed behavior (an event log), which hampers their applicability for large instances. This paper presents a fresh view to the alignment problem: the computation of alignments is casted as the resolution of Integer Linear Programming models, where the user can decide the granularity of the alignment steps. Moreover, a novel recursive strategy is used to split
the problem into small pieces, exponentially reducing the complexity of the ILP models to be solved. The contributions of this paper represent a promising alternative to fight the inherent complexity of computing alignments for large instances.Peer ReviewedPostprint (author's final draft
PetriBaR: A MATLAB Toolbox for Petri Nets Implementing Basis Reachability Approaches
This paper presents a MATLAB toolbox, called PetriBaR, for the analysis and control of Petri nets. PetriBaR is a package of functions devoted to basic Petri net analysis (including the computation of T-invariants, siphons, reachability graph, etc.), monitor design, reachability analysis, state estimation, fault diagnosis, and opacity verification. In particular, the functions for reachability analysis, state estimation, fault diagnosis, and opacity verification exploit the construction of the Basis Reachability Graph to avoid the exhaustive enumeration of the reachable set, thus leading to significant advantages in terms of computational complexity. All functions of PetriBaR are introduced in detail clarifying the syntax to be used to run them. Finally, they are illustrated via a series of numerical examples. PetriBaR is available online for public access
Petri Nets at Modelling and Control of Discrete-Event Systems Containing Nondeterminism - Part 1
Discrete-Event Systems are discrete in nature, driven by discrete events. Petri Nets are one of the mostly used tools for their modelling and control synthesis. Place/Transitions Petri Nets, Timed Petri Nets, Controlled Petri Nets are suitable when a modelled object is deterministic. When the system model contains uncontrollable/unobservable transitions and unobservable/unmeasurable places or other failures, such kinds of Petri Nets are insufficient for the purpose. In such a case Labelled Petri Nets and/or Interpreted Petri Nets have to be used. Particularities and mutual differences of individual kinds of Petri Nets are pointed out and their applicability to modelling and control of Discrete-Event Systems are described and tested
Minimum Initial Marking Estimation in Labeled Petri Nets With Unobservable Transitions
In the literature, researchers have been studying the minimum initial marking (MIM) estimation problem in the labeled Petri nets with observable transitions. This paper extends the results to labeled Petri nets with unobservable transitions (with certain special structure) and proposes algorithms for the MIM estimation (MIM-UT). In particular, we assume that the Petri net structure is given and the unobservable transitions in the net are contact-free. Based on the observation of a sequence of labels, our objective is to find the set of MIM(s) that is(are) able to produce this sequence and has(have) the smallest total number of tokens. An algorithm is developed to find the set of MIM(s) with polynomial complexity in the length of the observed label sequence. Two heuristic algorithms are also proposed to reduce the computational complexity. An illustrative example is also provided to demonstrate the proposed algorithms and compare their performance
Diagnosability Analysis of Labeled Time Petri Net Systems
In this paper, we focus on two notions of diagnosability
for labeled Time Petri net (PN) systems:
K-diagnosability implies that any fault occurrence
can be detected after at most K observations, while
Ď„-diagnosability implies that any fault occurrence can
be detected after at most Ď„ time units. A procedure to
analyze such properties isprovided.The proposedapproach
uses the Modified State Class Graph, a graph the authors
recently introduced for the marking estimation of labeled
Time PN systems,which providesan exhaustive description
of the system behavior. A preliminary diagnosabilty analysis
of the underlying logic system based on classical
approaches taken from the literature is required. Then, the
solution of some linear programming problems should
be performed to take into account the timing constraints
associated with transitions
Automated error correction of business process models
As order dependencies between process tasks can get complex, it is easy to make mistakes in process model design, especially behavioral ones such as deadlocks. Notions such as soundness formalize behavioral errors and tools exist that can identify such errors. However these tools do not provide assistance with the correction of the process models. Error correction can be very challenging as the intentions of the process modeler are not known and there may be many ways in which an error can be corrected. We present a novel technique for automatic error correction in process models based on simulated annealing. Via this technique a number of process model alternatives are identified that resolve one or more errors in the original model. The technique is implemented and validated on a sample of industrial process models. The tests show that at least one sound solution can be found for each input model within a reasonable response time
Conformance Checking of Mixed-paradigm Process Models
Mixed-paradigm process models integrate strengths of procedural and
declarative representations like Petri nets and Declare. They are specifically
interesting for process mining because they allow capturing complex behaviour
in a compact way. A key research challenge for the proliferation of
mixed-paradigm models for process mining is the lack of corresponding
conformance checking techniques. In this paper, we address this problem by
devising the first approach that works with intertwined state spaces of
mixed-paradigm models. More specifically, our approach uses an alignment-based
replay to explore the state space and compute trace fitness in a procedural
way. In every state, the declarative constraints are separately updated, such
that violations disable the corresponding activities. Our technique provides
for an efficient replay towards an optimal alignment by respecting all
orthogonal Declare constraints. We have implemented our technique in ProM and
demonstrate its performance in an evaluation with real-world event logs.Comment: Accepted for publication in Information System
Fault detection for discrete event systems using Petri nets with unobservable transitions
In this paper we present a fault detection approach for discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. Our diagnosis approach is based on the notions of basis marking and justification, that allow us to characterize the set of markings that are consistent with the actual observation, and the set of unobservable transitions whose firing enable it. This approach applies to all net systems whose unobservable subnet is acyclic. If the net system is also bounded the proposed approach may be significantly simplified by moving the most burdensome part of the procedure off-line, thanks to the construction of a graph, called the basis reachability graph
- …