Conformance checking is a fundamental task of process mining, which quantifies the extent to which the observed process executions match a normative process model. The state-of-the-art approaches compute alignments by exploring the state space formed by the synchronous product of the process model and the trace. This often leads to state space explosion, particularly when the model exhibits a high degree of choice and concurrency. Moreover, as alignments inherently impose a sequential structure, they fail to fully represent the concurrent behavior present in many real-world processes. To address these limitations, this paper proposes a new technique for computing partial-order alignments {on the fly using directed Petri net unfoldings, named FoldA. We evaluate our technique on 485 synthetic model-log pairs and compare it against Astar- and Dijkstra-alignments on 13 real-life model-log pairs and 6 benchmark pairs. The results show that our unfolding alignment, although it requires more computation time, generally reduces the number of queued states and provides a more accurate representation of concurrency.

Long event sequences (termed traces) and large data logs that originate from sensors and prediction models are becoming increasingly common in our data-rich world. In such scenarios, conformance checking-validating a data log against an expected system behavior (the process model) can become computationally infeasible due to the exponential complexity of finding an optimal alignment. To alleviate scalability challenges for this task, we propose ConLES, a sliding-window conformance checking approach for long event sequences that preserves the interpretability of alignment-based methods. ConLES partitions traces into manageable subtraces and iteratively aligns each against the expected behavior, leading to significant reduction of the search space while maintaining overall accuracy. We use global information that captures structural properties of both the trace and the process model, enabling informed alignment decisions and discarding unpromising alignments, even if they appear locally optimal. Performance evaluations across multiple datasets highlight that ConLES outperforms the leading optimal and heuristic algorithms for long traces, consistently achieving the optimal or near-optimal solution. Unlike other conformance methods that struggle with long event sequences, ConLES significantly reduces the search space, scales efficiently, and uniquely supports both predefined and discovered process models, making it a viable and leading option for conformance checking of long event sequences.

Long traces and large event logs that originate from sensors and prediction models are becoming more common in our data-rich world. In such circumstances, conformance checking, a key task in process mining, can become computationally infeasible due to the exponential complexity of finding an optimal alignment. This paper introduces a novel sliding window approach to address these scalability challenges while preserving the interpretability of alignment-based methods. By breaking down traces into manageable subtraces and iteratively aligning each with the process model, our method significantly reduces the search space. The approach uses global information that captures structural properties of the trace and the process model to make informed alignment decisions, discarding unpromising alignments even if they are optimal for a local subtrace. This improves the overall accuracy of the results. Experimental evaluations demonstrate that the proposed method consistently finds optimal alignments in most cases and highlight its scalability. This is further supported by a theoretical complexity analysis, which shows the reduced growth of the search space compared to other common conformance checking methods. This work provides a valuable contribution towards efficient conformance checking for large-scale process mining applications.

With the growing number of devices, sensors and digital systems, data logs may become uncertain due to, e.g., sensor reading inaccuracies or incorrect interpretation of readings by processing programs. At times, such uncertainties can be captured stochastically, especially when using probabilistic data classification models. In this work we focus on conformance checking, which compares a process model with an event log, when event logs are stochastically known. Building on existing alignment-based conformance checking fundamentals, we mathematically define a stochastic trace model, a stochastic synchronous product, and a cost function that reflects the uncertainty of events in a log. Then, we search for an optimal alignment over the reachability graph of the stochastic synchronous product for finding an optimal alignment between a model and a stochastic process observation. Via structured experiments with two well-known process mining benchmarks, we explore the behavior of the suggested stochastic conformance checking approach and compare it to a standard alignment-based approach as well as to an approach that creates a lower bound on performance. We envision the proposed stochastic conformance checking approach as a viable process mining component for future analysis of stochastic event logs.

In Markov Decision Processes (MDPs), the reward obtained in a state is Markovian, i.e., depends on the last state and action. This dependency makes it difficult to reward more interesting long-term behaviors, such as always closing a door after it has been opened, or providing coffee only following a request. Extending MDPs to handle non-Markovian reward functions was the subject of two previous lines of work. Both use LTL variants to specify the reward function and then compile the new model back into a Markovian model. Building on recent progress in temporal logics over finite traces, we adopt LDLf for specifying non-Markovian rewards and provide an elegant automata construction for building a Markovian model, which extends that of previous work and offers strong minimality and compositionality guarantees.