Parallel Learning of Automatic Classes of Languages

We introduce and explore a model for parallel learning of families of languages computable by finite automata. In this model, an algorithmic or automatic learner takes on n different input languages and identifies at least m of them correctly. For finite parallel learning, for large enough families, we establish a full characterization of learnability in terms of characteristic samples of languages. Based on this characterization, we show that it is the difference n − m, the number of languages which are potentially not identified, which is crucial. Similar results are obtained also for parallel learning in the limit. We consider also parallel finite learnability by finite automata and obtain some partial results. A number of problems for automatic variant of parallel learning remain open.

[1]  Efim B. Kinber,et al.  Frequency Computation and Bounded Queries , 1996, Theor. Comput. Sci..

[2]  Robert H. Sloan,et al.  BOOK REVIEW: "SYSTEMS THAT LEARN: AN INTRODUCTION TO LEARNING THEORY, SECOND EDITION", SANJAY JAIN, DANIEL OSHERSON, JAMES S. ROYER and ARUN SHARMA , 2001 .

[3]  Daniel Leivant,et al.  Logic and Computational Complexity , 1995, Lecture Notes in Computer Science.

[4]  Carl H. Smith,et al.  Training Sequences , 1989, Theor. Comput. Sci..

[5]  Volker Diekert,et al.  Regular frequency computations , 2005, Theor. Comput. Sci..

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

[7]  Rusins Freivalds,et al.  On the Power of Probabilistic Strategies in Inductive Inference , 1984, Theor. Comput. Sci..

[8]  Carl H. Smith,et al.  On Learning Multiple Concepts in Parallel , 1995, J. Comput. Syst. Sci..

[9]  Mark A. Fulk.  Prudence and Other Conditions on Formal Language Learning , 1990, Inf. Comput..

[10]  E. Kinber.  Frequency computations in finite automata , 1976 .

[11]  Carl H. Smith,et al.  The Power of Pluralism for Automatic Program Synthesis , 1982, JACM.

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

[13]  Rusins Freivalds,et al.  Frequency Prediction of Functions , 2011, MEMICS.

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

[15]  Klaus P. Jantke,et al.  Analogical and Inductive Inference , 1986, Lecture Notes in Computer Science.

[16]  P. Hall.  On Representatives of Subsets , 1935 .

[17]  Thomas Zeugmann,et al.  Types of monotonic language learning and their characterization , 1992, COLT '92.

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

[19]  Leonard Pitt,et al.  Probabilistic inductive inference , 1989, JACM.

[20]  Petr Hliněný,et al.  Mathematical and Engineering Methods in Computer Science , 2012, Lecture Notes in Computer Science.

[21]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

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

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

[24]  Thomas Zeugmann,et al.  Language learning in dependence on the space of hypotheses , 1993, COLT '93.

[25]  Yasuhito Mukouchi,et al.  Characterization of Finite Identification , 1992, AII.

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