Identification of unions of languages drawn from an identifiable class
COLT '89 Proceedings of the second annual workshop on Computational learning theory
The correct definition of finite elasticity: corrigendum to identification of unions
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
From wqo to bqo, via Ellentuck's theorem
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
Ordinal mind change complexity of language identification
Theoretical Computer Science
Properties of Language Classes With Finite Elasticity
ALT '93 Proceedings of the 4th International Workshop on Algorithmic Learning Theory
Algebraic Theory of Automata & Languages
Algebraic Theory of Automata & Languages
Learning indexed families of recursive languages from positive data: A survey
Theoretical Computer Science
Developments from enquiries into the learnability of the pattern languages from positive data
Theoretical Computer Science
Computational Commutative Algebra 1
Computational Commutative Algebra 1
On the origins of bisimulation and coinduction
ACM Transactions on Programming Languages and Systems (TOPLAS)
Commutative Regular Shuffle Closed Languages, Noetherian Property, and Learning Theory
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Elements of Automata Theory
Mind change efficient learning
Information and Computation
Theoretical Computer Science
Topological properties of concept spaces (full version)
Information and Computation
Extremal Combinatorics: With Applications in Computer Science
Extremal Combinatorics: With Applications in Computer Science
| Hi-index | 5.23 |
By reformulating a learning process of a set system L as a game between Teacher and Learner, we define the order type of L to be the order type of the game tree, if the tree is well-founded. The features of the order type of L (dimL in symbol) are (1) we can represent any well-quasi-order (wqo for short) by the set system L of the upper-closed sets of the wqo such that the maximal order type of the wqo is equal to dimL; (2) dimL is an upper bound of the mind-change complexity of L. dimL is defined iff L has a finite elasticity (fe for short), where, according to computational learning theory, if an indexed family of recursive languages has fe then it is learnable by an algorithm from positive data. Regarding set systems as subspaces of Cantor spaces, we prove that fe of set systems is preserved by any continuous function which is monotone with respect to the set-inclusion. By it, we prove that finite elasticity is preserved by various (nondeterministic) language operators (Kleene-closure, shuffle-closure, union, product, intersection, ...). The monotone continuous functions represent nondeterministic computations. If a monotone continuous function has a computation tree with each node followed by at most n immediate successors and the order type of a set system L is @a, then the direct image of L is a set system of order type at most n-adic diagonal Ramsey number of @a. Furthermore, we provide an order-type-preserving contravariant embedding from the category of quasi-orders and finitely branching simulations between them, into the complete category of subspaces of Cantor spaces and monotone continuous functions having Girard's linearity between them.