A Negative Result on Inductive Inference of Extended Pattern Languages
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The question of learnability of the class of extended pattern languages is considered to be one of the eldest and outstanding open problems in inductive inference of formal languages. This paper provides an appropriate answer presenting a subclass - the terminal-free extended pattern languages - that is not learnable in the limit. In order to achieve this result we will have to limit the respective alphabet of terminal symbols to exactly two letters. In addition we will focus on the impact of ambiguity of pattern languages on inductive inference of terminal-free extended pattern languages. The conventional view on nondeterminism in patterns inspired by formal language theory is transformed into an approach that meets the requirements of inductive inference. These studies will lead to some useful learnability criteria for classes of terminal-free extended pattern languages.
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- [Ang79]D. Angluin. Finding patterns common to a set of strings. In Proceedings, 11th Annual ACM Symposium on Theory of Computing, pages 130–141, 1979.Google Scholar
- [BCJ96]G.R. Baliga, J. Case, and S. Jain. Synthesizing enumeration techniques for language learning. In Proceedings of the Ninth Annual Conference on Computational Learning Theory, pages 169–180, 1996.Google Scholar
- [CL82]J. Case and L. Lynes. Machine inductive inference and language identification. In Lecture Notes in Computer Science, volume 140, pages 107–115. Proceeedings of the 9th International Colloquium on Automata, Languages and Programming, 1982.Google Scholar
- [Mit98]A.R. Mitchell. Learnability of a subclass of extended pattern languages. In Proceedings of the Eleventh Annual Conference on Computational Learning Theory, pages 64–71, 1998.Google Scholar
- [MS94]A. Mateescu and A. Salomaa. Nondeterminism in patterns. In Lecture Notes in Computer Science, volume 775, pages 661–668. STACS 94, 11th Annual Symposium on Theoretical Aspects of Computer Science, 1994.Google Scholar
- [Rog92]H. Rogers. Theory of Recursive Functions and Effective Computability. MIT Press, 1992. 3. print.Google Scholar
- [Shi82a]T. Shinohara. Polynomial time inference of extended regular pattern languages. In Lecture Notes in Computer Science, volume 147, pages 115–127. RIMS Symposia on Software Science and Engineering, Proceedings, Kyoto, 1982.Google Scholar
- [Shi82b]T. Shinohara. Polynomial time inference of pattern languages and its application. In Proceedings of the 7th IBM Symposium on Mathematical Foundations of Computer Science, pages 191–209, 1982.Google Scholar
- [Wri89]K. Wright. Identification of unions of languages drawn from an identifiable class. In Proceedings of the Second Annual Workshop on Computational Learning Theory, pages 328–333, 1989.Google Scholar