The reconstruction of models from experimental data is a challenging problem due to the inherited complexity of biological systems. We developed an exact, exclusively data-driven approach to reconstruct Petri nets from experimental time-series data. Our approach aims at reconstructing all such netwoks that fit the given experimental data, to provide all possible alternatives of mechanisms behind the experimental observations, which typically results in a large set of solution alternatives. To

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... ep this solution set reasonably small while still guaranteeing its completeness, we firstly generate only Petri nets being minimal in the sense that all other networks fitting the data contain the reconstructed ones. We further aim at avoiding the generation of minimal solutions which are "technically correct" but would be ruled out later during a subsequent verification process to check whether the returned solutions are "biological meaningful" or even contradict well-established biological knowledge. For that, we propose to extent the considered input (beyond the information given with the experimental time-series data) for the reconstruction process and demonstrate with the help of a running example the influence on the generated solution set.