This is a correction to Thuijsman and Reniers (2022).

In a continuation on Thuijsman and Reniers (2022), it was pointed out by an anonymous reviewer that our implementation used for the experiments contained a mistake. We are very grateful to this reviewer for pointing out this mistake. We realized that the implementation of Thuijsman and Reniers (2022) contained the same mistake.

Although the algorithms were still functionally correct, because of the mistake their computational efficiency was significantly worse than that of a proper implementation. Since Thuijsman and Reniers (2022) aims to improve computational efficiency, and uses experiments to indicate that improvement, the implementation should be properly efficient. Note that the theoretical parts of Thuijsman and Reniers (2022) are still correct, the mistake only affects the timing measurements in the experimental part of the paper.

However, because the mistake has a significant impact on the timing measurements, we present this correction. In this correction we explain the mistake, present the new results, and update our conclusions based on the new results.

In particular, the reachability search algorithms (Algorithms 3 and 4 in Thuijsman and Reniers (2022)) were not properly implemented. This is because an inappropriate data structure was used to store the transition relation. In the erroneous implementation, an edge list structure was used: a list of triples, each specifying an origin state, event, and target state. Using an edge list, each time the neighbors of some state are evaluated (e.g., lines 6-7 in Algorithm 3 of Thuijsman and Reniers (2022)), an iteration is performed over all transitions, leading to a complexity of \(O(|X|\cdot |\longrightarrow |)\) for the algorithm overall. Instead, the transition relation should be stored using an adjacency list: each index in the list corresponds to a state index and stores all neighbors of that state. When an adjacency list is used, no iteration is required to find the neighbors of a state, and a complexity of \(O(|X|+|\longrightarrow |)\) for the reachability search can be obtained (Kleinberg and Tardos , 2005).

The implementation has been corrected. The code repositoryFootnote 1 we refer to in Thuijsman and Reniers (2022) has been updated accordingly. We have repeated the experiments from Thuijsman and Reniers (2022). Tables 1, 2, and 3 respectively present the updated results relative to Tables 1, 2, and 3 in Thuijsman and Reniers (2022). Each runtime value we present in this correction is the mean runtime over 100 executions of the experiment.

Table 1 Experimental results of performing \(\text { {\texttt {SS}}}\), \(\text { {\texttt {ITSS}}}\), and \(\text { {\texttt {GTSS}}}\) on five variant models of the Transfer Line model
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Table 2 Experimental results of performing \(\text { {\texttt {SS}}}\) and \(\text { {\texttt {GTSS}}}\) for evolution of the complete Component B Wafer Logistics model
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Table 3 Experimental results of performing \(\text { {\texttt {SS}}}\) and \(\text { {\texttt {GTSS}}}\) for evolution of the reachable part of the Component B Wafer Logistics model
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We observe that in almost all experimental cases Transformational Supervisor Synthesis (TSS) requires more runtime than basic Supervisor Synthesis (SS). Perhaps in some particular cases, TSS may be quicker than SS. However, based on these updated experimental results, we must conclude that in practical cases TSS is generally less efficient than SS. Therefore, it is recommended to use SS over TSS, also for evolving systems.