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The constraint-based pattern discovery paradigm was introduced with the aim of providing to the user a tool to drive the discovery process towards potentially interesting patterns, with the positive side effect of achieving a more efficient computation. In this paper we review and extend the state-of-the-art of the constraints that can be pushed in a frequent pattern computation. We introduce novel data reduction techniques which are able to exploit convertible anti-monotone constraints (e.g.,doi:10.1016/j.datak.2006.02.006 fatcat:7p3zuyvgcbdofjy7bvpcarxsba