On the Amount of Nonconstructivity in Learning Formal Languages from Positive Data
Nonconstructive computations by various types of machines and automata have been considered by e.g., Karp and Lipton  and Freivalds [9, 10]. They allow to regard more complicated algorithms from the viewpoint of more primitive computational devices. The amount of nonconstructivity is a quantitative characterization of the distance between types of computational devices with respect to solving a specific problem.
This paper studies the amount of nonconstructivity needed to learn classes of formal languages from positive data. Different learning types are compared with respect to the amount of nonconstructivity needed to learn indexable classes and recursively enumerable classes, respectively, of formal languages from positive data. Matching upper and lower bounds for the amount of nonconstructivity needed are shown.
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- 3.Barzdin, J.: Inductive inference of automata, functions and programs. In: Proc. of the 20th International Congress of Mathematicians, Vancouver, Canada, pp. 455–460 (1974); republished in Amer. Math. Soc. Transl. 109 (2), 107– 112 (1977)Google Scholar
- 4.Bārzdiņš, J.M.: Complexity of programs to determine whether natural numbers not greater than n belong to a recursively enumerable set. Soviet Mathematics Doklady 9, 1251–1254 (1968)Google Scholar
- 15.Jain, S., Osherson, D., Royer, J.S., Sharma, A.: Systems that Learn: An Introduction to Learning Theory, 2nd edn. MIT Press, Cambridge (1999)Google Scholar
- 16.Jain, S., Stephan, F., Zeugmann, T.: On the amount of nonconstructivity in learning formal languages from text. Tech. Rep. TCS-TR-A-12-55, Division of Computer Science, Hokkaido University (2012)Google Scholar
- 22.Rogers Jr., H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill (1967); reprinted, MIT Press 1987Google Scholar
- 24.Zeugmann, T., Minato, S., Okubo, Y.: Theory of Computation. Corona Publishing Co, Ltd. (2009)Google Scholar