Automatic learning of subclasses of pattern languages

  • Authors:
  • John Case;Sanjay Jain;Trong Dao Le;Yuh Shin Ong;Pavel Semukhin;Frank Stephan

  • Affiliations:
  • Department of Computer and Information Sciences, University of Delaware, Newark, DE 19716-2586, USA;Department of Computer Science, National University of Singapore, Singapore 117417, Republic of Singapore;Department of Computer Science, National University of Singapore, Singapore 117417, Republic of Singapore;Department of Computer Science, National University of Singapore, Singapore 117417, Republic of Singapore;Department of Computer Science, University of Regina, Canada;Department of Computer Science and Department of Mathematics, National University of Singapore, Singapore 119076, Republic of Singapore

  • Venue:
  • Information and Computation
  • Year:
  • 2012

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Abstract

Automatic classes are classes of languages for which a finite automaton can decide the membership problem for the languages in the class, in a uniform way, given an index for the language. For alphabet size of at least 4, every automatic class of erasing pattern languages is contained, for some constant n, in the class of all languages generated by patterns which contain (1) every variable only once and (2) at most n symbols after the first occurrence of a variable. It is shown that such a class is automatically learnable using a learner with the length of the long-term memory being bounded by the length of the first example seen. The study is extended to show the learnability of related classes such as the class of unions of two pattern languages of the above type.