Nine-month-olds already display knowledge of the native phonotactics, namely react differently to licit versus illicit sound combinations. Children must thus rely on a remarkably efficient phonotactic learning procedure. What does it look like? Assume that the learner is provided with the typology of OT grammars corresponding to all rankings of a given constraint set. Data come in a stream and consist of licit phonological forms. The learner maintains a current constraint ranking, which is initialized with markedness above faithfulness constraints, yielding a restrictive initial phonotactics. Whenever the current ranking fails at accepting the current piece of data as licit, a slight re-ranking is performed, in the direction of a laxer phonotactics. The current piece of data is then discarded and the learner waits for the next piece of data to evaluate the performance of the updated ranking. This learner is called an error-driven ranking algorithm (EDRA) because the learning dynamics is driven by the errors made on the incoming stream of data. As EDRAs do not keep track of previously seen data, they are suited to model the precocious acquisition of phonotactics, prior to the development of the native language lexicon. An EDRA converges provided it eventually stops making mistakes and thus rests on a final ranking. Convergence is efficient provided the number of errors is not only finite but also small. The final grammar entertained at convergence is guaranteed to be consistent, namely to accept any form which is indeed licit. It could nonetheless fail at restrictiveness, namely it could fail at rejecting forms which are instead illicit. This class develops the computational theory of the EDRA model of the acquisition of phonotactics, focusing on convergence, efficiency, consistency, and restrictiveness.