On Piecewise Testable, Starfree, and Recognizable Picture Languages

We isolate a technique for showing that a picture language (i.e. a“two-dimensional language/rd) is not recognizable. Then we prove the non-recognizability of a picture language that is both starfree (i.e., definable by means of union, concatenation, and complement) and piecewise testable (i.e., definable by means of allowed subpictures), solving an open question in [GR96].