Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete finite prefix of a P/T Petri net’s unfolding contains all information to verify, e.g., reachability of markings. We unite these two concepts and define complete finite prefixes of the symbolic unfolding of high-level Petri nets. For a class of safe high-level Petri nets, we generalize the well-known algorithm by Esparza et al. for constructing small such prefixes. We evaluate this extended algorithm through a prototype implementation on four novel benchmark families. Additionally, we identify a more general class of nets with infinitely many reachable markings, for which an approach with an adapted cut-off criterion extends the complete prefix methodology, in the sense that the original algorithm cannot be applied to the P/T net represented by a high-level net.

Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete finite prefix of a P/T Petri net's unfolding contains all information to verify, e.g., reachability of markings. We unite these two concepts and define complete finite prefixes of the symbolic unfolding of high-level Petri nets. For a class of safe high-level Petri nets, we generalize the well-known algorithm by Esparza et al. for constructing small such prefixes. We evaluate this extended algorithm through a prototype implementation on four novel benchmark families. Additionally, we identify a more general class of nets with infinitely many reachable markings, for which an approach with an adapted cut-off criterion extends the complete prefix methodology, in the sense that the original algorithm cannot be applied to the P/T net represented by a high-level net. Comment: This is a revised and extended version of "Nick W\"urdemann, Thomas Chatain, Stefan Haar: Taking Complete Finite Prefixes to High Level, Symbolically. Petri Nets 2023: 123-144"

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. In this paper, we set our problem of timed alignment and solve two cases each corresponding to a different metric over time processes.

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.

Parameter synthesis for timed systems aims at deriving parameter valuations satisfying a given property. In this article, we target concurrent systems. We use partial-order semantics for parametric time Petri nets as a way to both cope with the well-known state-space explosion due to concurrency and significantly enhance the result of an existing synthesis algorithm. Given a reference parameter valuation, our approach synthesizes other valuations preserving the partial-order executions of the reference parameter valuation. We show the applicability of our approach using a tool applied to asynchronous circuits.

Conformance checking techniques asses the suitability of a process model in representing an underlying process, observed through a collection of real executions. These techniques suffer from the well-known state space explosion problem, hence handling process models exhibiting large or even infinite state spaces remains a challenge. One important metric in conformance checking is to asses the precision of the model with respect to the observed executions, i.e., characterize the ability of the model to produce behavior unrelated to the one observed. By avoiding the computation of the full state space of a model, current techniques only provide estimations of the precision metric, which in some situations tend to be very optimistic, thus hiding real problems a process model may have. In this paper we present the notion of anti-alignment as a concept to help unveiling traces in the model that may deviate significantly from the observed behavior. Using anti-alignments, current estimations can be improved, e.g., in precision checking. We show how to express the problem of finding anti-alignments as the satisfiability of a Boolean formula, and provide a tool which can deal with large models efficiently. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Occurrence nets are a well known partial order model for the concurrent behavior of Petri nets. The causality and conflict relations between events, which are explicitly represented in occurrence nets, induce logical dependencies between event occurrences: the occurrence of an event e in a run implies that all its causal predecessors also occur, and that no event in conflict with e occurs. But these structural relations do not express all the logical dependencies between event occurrences in maximal runs: in particular, the occurrence of e in any maximal run may imply the occurrence of another event that is not a causal predecessor of e, in that run. The reveals relation has been introduced to express this dependency between two events. Here we generalize the reveals relation to express more general dependencies, involving more than two events, and we introduce ERL logic to express them as boolean formulas. Finally we answer the synthesis problem that arises: given an ERL formula �, is there an occurrence net 𝒩 such that � describes exactly the dependencies between the events of 𝒩?

Real-time distributed systems may be modeled in different formalisms such as time Petri nets (TPN) and networks of timed automata (NTA). This paper focuses on translating a 1-bounded TPN into an NTA and considers an equivalence which takes the distribution of actions into account. This translation is extensible to bounded TPNs. We first use S-invariants to decompose the net into components that give the structure of the automata, then we add clocks to provide the timing information. Although we have to use an extended syntax in the timed automata, this is a novel approach since the other transformations and comparisons of these models did not consider the preservation of concurrency.

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