Systems that learn: an introduction to learning theory for cognitive and computer scientists
Systems that learn: an introduction to learning theory for cognitive and computer scientists
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
An Introduction to the General Theory of Algorithms
An Introduction to the General Theory of Algorithms
Machine Inductive Inference and Language Identification
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Journal of Computer and System Sciences
Learning multiple languages in groups
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
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We consider a variant of Gold's learning paradigm where a learner receives as input n different languages (in the form of one text where all input languages are interleaved). Our goal is to explore the situation when a more ''coarse'' classification of input languages is possible, whereas more refined classification is not. More specifically, we answer the following question: under which conditions, a learner, being fed n different languages, can produce m grammars covering all input languages, but cannot produce k grammars covering input languages for any km. We also consider a variant of this task, where each of the output grammars may not cover more than r input languages. Our main results indicate that the major factor affecting classification capabilities is the difference n-m between the number n of input languages and the number m of output grammars. We also explore the relationship between classification capabilities for smaller and larger groups of input languages. For the variant of our model with the upper bound on the number of languages allowed to be represented by one output grammar, for classes consisting of disjoint languages, we found complete picture of relationship between classification capabilities for different parameters n (the number of input languages), m (number of output grammars), and r (bound on the number of languages represented by each output grammar). This picture includes a combinatorial characterization of classification capabilities for the parameters n,m,r of certain types.