The main advantages of Tarjan's strongly connected component (SCC) algorithm are its linear time complexity and ability to return SCCs on-the-fly, while traversing or even generating the graph. Until now, most parallel SCC algorithms sacrifice both: they run in quadratic worst-case time and/or require the full graph in advance.

We investigate and improve the scalability of multi-core LTL model checking. Our algorithm, based on parallel DFS-like SCC decomposition, is able to efficiently decompose large SCCs on-the-fly, which is a difficult problem to solve in parallel.To validate the algorithm we performed experiments on a 64-core machine. We used an extensive set of well-known benchmark collections obtained from the BEEM database and the Model Checking Contest. We show that the algorithm is competitive with the current state-ofthe-art model checking algorithms. For larger models we observe that our algorithm outperforms the competitors. We investigate how graph characteristics relate to and pose limitations on the achieved speedups.

Conformance checking is a branch of process mining that aims to assess to what degree event data originating from the execution of a (business) process and a corresponding reference model conform to each other. Alignments have been recently introduced as a solution for conformance checking and have since rapidly developed into becoming the de facto standard. The state-of-the-art method to compute alignments is based on solving a shortest path problem derived from the reference model and the event data. Within such a shortest path problem, a cost function is used to guide the search to an optimal solution. The standard cost-function treats mismatches in the model and log as equal. In this paper, we consider a variant of this standard cost function which maximizes the number of correct matches instead. We study the effects of using this cost-function compared to the standard cost function on both small and large models using over a thousand generated and industrial case studies. We further show that the alignment computation process can be sped up significantly in specific instances. Finally, we present a new algorithm for the computation of alignments on models with many log traces that is an order of magnitude faster (in maximizing synchronous moves) compared to the state-of-the-art A* based solution method, as a result of a preprocessing step on the model.

Conformance checking is a branch of process mining that aims to assess to what degree a given set of log traces and a corresponding reference model conform to each other. The state-of-the-art approach in conformance checking is based on the concept of alignments. Alignments express the observed behaviour in terms of the reference model while minimizing the number of mismatches between the event data and the model. The currently known best algorithm for constructing alignments applies the A* shortest path algorithm for each trace of event data. In this work, we apply insights from the field of model checking to aid conformance checking. We investigate whether alignments can be computed efficiently via symbolic reachability with decision diagrams. We designed a symbolic algorithm for computing shortest-paths on graphs restricted to 0-and 1-cost edges (which is typical for alignments). We have implemented our approach in the LTSMIN model checking toolset and compare its performance with the A* implementation supported by ProM. We generated more than 4000 experiments (Petri net model and log trace combinations) by setting various parameters, and analysed performance and related these to structural properties. Our empirical study shows that the symbolic technique is in general better suited for computing alignments on large models than the A* approach. Our approach is better performing in cases where the size of the state-space tends to blow up. Based on our experiments we conclude that the techniques are complementary, since there is a significant number of cases where A* outperforms the symbolic technique and vice versa.

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