Automatic Learning from Repetitive Texts

We study the connections between the learnability of automatic families of languages and the types of text used to present them to a learner. More precisely, we study how restrictions on the number of times that a correct datum appears in a text influence what classes of languages are automatically learnable. We show that an automatic family of languages is automatically learnable from fat text iff it is automatically learnable from thick text iff it is verifiable from balanced text iff it satisfies Angluin’s tell-tale condition. Furthermore, many automatic families are automatically learnable from exponential text. We also study the relationship between automatic learnability and verifiability and show that all automatic families are automatically partially verifiable from exponential text and automatically learnable from thick text.

[1]  Leonard Pitt,et al.  Inductive Inference, DFAs, and Computational Complexity , 1989, AII.

[2]  Achim Blumensath,et al.  Automatic structures , 2000, Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332).

[3]  Henning Fernau,et al.  Identification of function distinguishable languages , 2000, Theor. Comput. Sci..

[4]  Satoshi Kobayashi,et al.  Locality, Reversibility, and Beyond: Learning Languages from Positive Data , 1998, ALT.

[5]  Efim B. Kinber.  Learning Regular Expressions from Representative Examples and Membership Queries , 2010, ICGI.

[6]  Leonard Pitt,et al.  A polynomial-time algorithm for learning k-variable pattern languages from examples , 1989, COLT '89.

[7]  Sanjay Jain,et al.  Learnability of automatic classes , 2012, J. Comput. Syst. Sci..

[8]  Hiroki Arimura,et al.  Inductive Inference of Unbounded Unions of Pattern Languages from Positive Data , 1996, ALT.

[9]  Dana Angluin,et al.  Inference of Reversible Languages , 1982, JACM.

[10]  Thomas Zeugmann,et al.  Learning indexed families of recursive languages from positive data: A survey , 2008, Theor. Comput. Sci..

[11]  Sandra Zilles,et al.  Learning Relational Patterns , 2011, ALT.

[12]  Eliana Minicozzi,et al.  Some Natural Properties of Strong-Identification in Inductive Inference , 1976, Theor. Comput. Sci..

[13]  E. Mark Gold,et al.  Language Identification in the Limit , 1967, Inf. Control..

[14]  Anil Nerode,et al.  Automatic Presentations of Structures , 1994, LCC.

[15]  John Case,et al.  Automatic Learners with Feedback Queries , 2011, CiE.

[16]  John Case,et al.  Automatic Learning of Subclasses of Pattern Languages , 2011, LATA.

[17]  Rolf Wiehagen,et al.  Ignoring data may be the only way to learn efficiently , 1994, J. Exp. Theor. Artif. Intell..

[18]  Kenneth Wexler,et al.  Formal Principles of Language Acquisition , 1980 .

[19]  Dana Angluin,et al.  Finding Patterns Common to a Set of Strings , 1980, J. Comput. Syst. Sci..

[20]  Klaus P. Jantke.  Monotonic and non-monotonic inductive inference , 2009, New Generation Computing.

[21]  Dana Angluin,et al.  Learning Regular Sets from Queries and Counterexamples , 1987, Inf. Comput..

[22]  Daniel N. Osherson,et al.  Systems That Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists , 1990 .

[23]  Timo Kötzing,et al.  Learning in the limit with lattice-structured hypothesis spaces , 2012, Theor. Comput. Sci..

[24]  Rolf Wiehagen,et al.  Language Learning from Texts: Degrees of Intrinsic Complexity and Their Characterizations , 2000, J. Comput. Syst. Sci..

[25]  Rolf Wiehagen,et al.  Polynomial-time inference of arbitrary pattern languages , 2009, New Generation Computing.

[26]  Hiroki Arimura,et al.  Inductive inference of unbounded unions of pattern languages from positive data , 2000, Theor. Comput. Sci..

[27]  Carl H. Smith,et al.  On the impact of forgetting on learning machines , 1995, JACM.

[28]  Setsuo Arikawa,et al.  Towards a Mathematical Theory of Machine Discovery from Facts , 1995, Theor. Comput. Sci..

[29]  Frank Stephan,et al.  Learning algebraic structures from text , 2001, Theor. Comput. Sci..

[30]  Carl H. Smith,et al.  Learning via queries , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[31]  Wei Luo,et al.  Mind change efficient learning , 2006, Inf. Comput..

[32]  Achilles Beros.  Anomalous Vacillatory Learning , 2013, J. Symb. Log..

[33]  John Case,et al.  Difficulties in Forcing Fairness of Polynomial Time Inductive Inference , 2009, ALT.

[34]  J. van Leeuwen.  Algorithmic Learning Theory , 1999, Lecture Notes in Computer Science.

[35]  Sasha Rubin,et al.  Automata Presenting Structures: A Survey of the Finite String Case , 2008, Bulletin of Symbolic Logic.

[36]  John Case,et al.  Automatic functions, linear time and learning , 2013, Log. Methods Comput. Sci..

[37]  Dana Angluin,et al.  Inductive Inference of Formal Languages from Positive Data , 1980, Inf. Control..

[38]  Gunter Grieser.  Reflective Inductive Inference of Recursive Functions , 2002, ALT.

[39]  Sanjay Jain,et al.  ON AUTOMATIC FAMILIES , 2011 .

[40]  Klaus Ambos-Spies,et al.  Inductive inference and computable numberings , 2011, Theor. Comput. Sci..

[41]  Manuel Blum,et al.  Toward a Mathematical Theory of Inductive Inference , 1975, Inf. Control..

[42]  Frank Stephan,et al.  Language Learning from Texts: Mind Changes, Limited Memory and Monotonicity (Extended Abstract). , 1995, COLT 1995.

[43]  Bernard R. Hodgson.  On Direct Products of Automaton Decidable Theories , 1982, Theor. Comput. Sci..

[44]  Sanjay Jain,et al.  Inductive inference and reverse mathematics , 2016, Ann. Pure Appl. Log..

[45]  Gisela Schäfer-Richter,et al.  Über Eingabeabhängigkeit und Komplexität von Inferenzstrategien , 1984 .