Undecidability of existential properties in picture languages

Abstract We are interested in the description of a set of pictures by string languages by using several semantics: segments [12] , segments with blank moves [8] and pixels [10] . We give a method to code the Post correspondence problem in rational picture languages in order to show the undecidability of existence of words satisfying a given property in a rational language. In particular, we study the properties like “is a self-avoiding word”, “is a minimal picture word” or “describes a connected picture”.