Abstract Process discovery is the problem of, given a log of observed behaviour, finding a process model that ‘best ’ describes this behaviour. A large variety of process discovery algorithms has been proposed. However, no existing algorithm guarantees to return a fitting model (i.e., able to reproduce all observed behaviour) that is sound (free of deadlocks and other anomalies) in finite time. We present an extensible framework to discover from any given log a set of block-structured process models that are sound and fit the observed behaviour. In addition we characterise the minimal information required in the log to rediscover a particu-lar process model. We then provide a polynomial-time algorithm for discovering a sound, fitting, block...