Given a timed automaton with parametric timings, our objective is to describe a procedure for deriving constraints on the parametric timings in order to ensure that, for each value of parameters satisfying these constraints, the behaviors of the timed automata are time-abstract equivalent. We will exploit a reference valuation of the parameters that is supposed to capture a characteristic proper behavior of the system. The method has been implemented and is illustrated on various examples of asynchronous circuits.

Abstract. The holy grail in process mining is an algorithm that, given an event log, produces fitting, precise, properly generalizing and simple process models. While there is consensus on the existence of solid metrics for fitness and simplicity, current metrics for precision and generalization have important flaws, which hamper their applicability in a general setting. In this paper, a novel approach to measure precision and generalization is presented, which relies on the notion of anti-alignments. An anti-alignment describes highly deviating model traces with respect to observed behavior. We propose metrics for precision and generalization that resemble the leave-one-out cross-validation techniques, where individual traces of the log are removed and the computed anti-alignment assess the model's capability to describe precisely or generalize the observed behavior.

Predicting biological systems’ behaviors requires taking into account many molecular and genetic elements for which limited information is available past a global knowledge of their pairwise interactions. Logical modeling, notably with Boolean Networks (BNs), is a well-established approach that enables reasoning on the qualitative dynamics of networks. Several dynamical interpretations of BNs have been proposed. The synchronous and (fully) asynchronous ones are the most prominent, where the value of either all or only one component can change at each step. Here we prove that, besides being costly to analyze, these usual interpretations can preclude the prediction of certain behaviors observed in quantitative systems. We introduce an execution paradigm, the Most Permissive Boolean Networks (MPBNs), which offers the formal guarantee not to miss any behavior achievable by a quantitative model following the same logic. Moreover, MPBNs significantly reduce the complexity of dynamical analysis, enabling to model genome-scale networks.

Abstract. Attractors of network dynamics represent the long-term behaviours of the modelled system. Their characterization is therefore crucial for understanding the response and differentiation capabilities of a dynamical system. In the scope of qualitative models of interaction networks, the computation of attractors reachable from a given state of the network faces combinatorial issues due to the state space explosion. In this paper, we present a new algorithm that exploits the concurrency between transitions of parallel acting components in order to reduce the search space. The algorithm relies on Petri net unfoldings that can be used to compute a compact representation of the dynamics. We illustrate the applicability of the algorithm with Petri net models of cell signalling and regulation networks, Boolean and multi-valued. The proposed approach aims at being complementary to existing methods for deriving the attractors of Boolean models, while being generic since it applies to any safe Petri net.

Certifying that a process model is aligned with the real process executions is perhaps the most desired feature a process model may have: aligned process models are crucial for organizations, since strategic decisions can be made easier on models instead of on plain data. In spite of its importance, the current algorithmic support for computing alignments is limited: either techniques that explicitly explore the model behavior (which may be worst-case exponential with respect to the model size), or heuristic approaches that cannot guarantee a solution, are the only alternatives. In this paper we propose a solution that sits right in the middle in the complexity spectrum of alignment techniques; it can always guarantee a solution, whose quality depends on the exploration depth used and local decisions taken at each step. We use linear algebraic techniques in combination with an iterative search which focuses on progressing towards a solution. The experiments show a clear reduction in the time required for reaching a solution, without sacrificing significantly the quality of the alignment obtained.

Abstract. 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 wellknown 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 antialignment 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.

Process mining techniques use event logs containing real process executions in order to mine, align and extend process models. The partition of an event log into trace variants facilitates the understanding and analysis of traces, so it is a common pre-processing in process mining environments. Trace clustering automates this partition; traditionally it has been applied without taking into consideration the availability of a process model. In this paper we extend our previous work on process model based trace clustering, by allowing cluster centroids to have a complex structure, that can range from a partial order, down to a subnet of the initial process model. This way, the new clustering framework presented in this paper is able to cluster together traces that are distant only due to concurrency or loop constructs in process models. We show the complexity analysis of the different instantiations of the trace clustering framework, and have implemented it in a prototype tool that has been tested on different datasets.

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