Ziyuan Gao

On Conservative Learning of Recursively Enumerable Languages

Conservative partial learning is a variant of partial learning whereby the learner, on a text for a target language L, outputs one index e with L = W e infinitely often and every further hypothesis d is output only finitely often and satisfies \(L \not\subseteq W_d\). The present paper studies the learning strength of this notion, comparing it with other learnability criteria such as confident partial learning, explanatory learning, as well as behaviourally correct learning. It is further established that for classes comprising infinite sets, conservative partial learnability is in fact equivalent to explanatory learnability relative to the halting problem.

Learning families of closed sets in matroids

In this paper it is studied for which oracles A and which types of A-r.e. matroids the class of all A-r.e. closed sets in the matroid is learnable by an unrelativised learner. The learning criteria considered comprise in particular criteria more general than behaviourally correct learning, namely behaviourally correct learning from recursive texts, partial learning and reliably partial learning. For various natural classes of matroids and learning criteria, characterisations of learnability are obtained.

Distinguishing pattern languages with membership examples

Abstract This article determines two learning-theoretic combinatorial parameters, the teaching dimension and the recursive teaching dimension, for various families of pattern languages over alphabets of varying size. Our results and formal proofs are of relevance to recent studies in computational learning theory as well as in formal language theory. This is an expanded and corrected version of an earlier paper by Mazadi et al. (2014).

Distinguishing Pattern Languages with Membership Examples

This article determines two learning-theoretic combinatorial parameters, the teaching dimension and the recursive teaching dimension, for various families of pattern languages over alphabets of varying size. Our results and formal proofs are of relevance to recent studies in computational learning theory as well as in formal language theory.

On the teaching complexity of linear sets

Abstract Linear sets are the building blocks of semilinear sets, which are in turn closely connected to automata theory and formal languages. Prior work has investigated the learnability of linear sets and semilinear sets in three models – Valiants PAC-learning model, Golds learning in the limit model, and Angluins query learning model. This paper considers teacher–learner models of learning families of linear sets, in which a benevolent teacher presents a set of labelled examples to the learner. First, we study the classical teaching model, in which a teacher must successfully teach any consistent learner. Second, we will apply a generalisation of the recently introduced recursive teaching model to several infinite classes of linear sets, and show that thus the maximum sample complexity of teaching these classes can be drastically reduced compared to classical teaching. To this end, a major focus of the paper will be on determining two relevant teaching parameters, the teaching dimension and recursive teaching dimension, for various families of linear sets.

Partial Learning of Recursively Enumerable Languages

This paper studies several typical learning criteria in the model of partial learning of r.e. sets in the recursion-theoretic framework of inductive inference. Its main contribution is a complete picture of how the criteria of confidence, consistency and conservativeness in partial learning of r.e. sets separate, also in relation to basic criteria of learning in the limit. Thus this paper constitutes a substantial extension to prior work on partial learning. Further highlights of this work are very fruitful characterisations of some of the inference criteria studied, leading to interesting consequences about the structural properties of the collection of classes learnable under these criteria. In particular a class is consistently partially learnable iff it is a subclass of a uniformly recursive family.

On the Teaching Complexity of Linear Sets

Linear sets are the building blocks of semilinear sets, which are in turn closely connected to automata theory and formal languages. Prior work has investigated the learnability of linear sets and semilinear sets in three models --- Valiants PAC-learning model, Golds learning in the limit model, and Angluins query learning model. This paper considers a teacher-learner model of learning families of linear sets, whereby the learner is assumed to know all the smallest sets

Classifying the Arithmetical Complexity of Teaching Models

T_1,T_2,\ldots