Closure Properties of Pattern Languages

  • Joel D. Day
  • Daniel Reidenbach
  • Markus L. Schmid
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8633)


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.


Pattern languages Closure properties 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Joel D. Day
    • 1
  • Daniel Reidenbach
    • 1
  • Markus L. Schmid
    • 2
  1. 1.Department of Computer ScienceLoughborough UniversityLoughboroughUK
  2. 2.FB IV–Abteilung InformatikwissenschaftenUniversität TrierTrierGermany

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