2134/16055 Joel Day Joel Day Daniel Reidenbach Daniel Reidenbach Markus L. Schmid Markus L. Schmid Closure properties of pattern languages Loughborough University 2014 Pattern languages Closure properties Information and Computing Sciences not elsewhere classified 2014-10-13 13:14:56 Conference contribution https://repository.lboro.ac.uk/articles/conference_contribution/Closure_properties_of_pattern_languages/9404873 Pattern languages are a well-established class of languages that is particularly popular in algorithmic learning theory, but very little is known about their closure properties. In the present paper we establish a large number of closure properties of the terminal-free pattern languages, and we characterise when the union of two terminal-free pattern languages is again a terminal-free pattern language. We demonstrate that the equivalent question for general pattern languages is characterised differently, and that it is linked to some of the most prominent open problems for pattern languages. We also provide fundamental insights into a well-known construction of E-pattern languages as unions of NE-pattern languages, and vice versa. © 2014 Springer International Publishing Switzerland.