The approach of ordinal mind change complexity, introduced by Freivalds and Smith, uses (notations for) constructive ordinals to bound the number of mind changes made by a learning machine. This approach provides a measure of the extent to which a learning machine has to keep revising its estimate of the number of mind changes it will make before converging to a correct hypothesis for languages in the class being learned. Recently, this notion, which also yields a measure for the difficulty of learning a class of languages, has been used to analyze the learnability of rich concept classes. Preprint submitted to Elsevier Science change bound if it has finite elasticity and can be identified by a conservative machine. It is also shown that the requirement of conservative identification can be sacrificed for the purely topological requirement of M-finite thickness. Interaction between identification by monotonic strategies and existence of ordinal mind change bound is also investigated.

Formal learning theory is one of several mathematical approaches to the study of intelligent adaptation to the environment. The analysis developed in this book is based on a number theoretical approach to learning and uses the tools of recursive-function theory to understand how learners come to an accurate view of reality. This revised and expanded edition of a successful text provides a comprehensive, self-contained introduction to the concepts and techniques of the theory. Exercises throughout the text provide experience in the use of computational arguments to prove facts about learning. Bradford Books imprint

A new investigation of the complexity of language identification is undertaken using the notion of reduction from recursion theory and complexity theory. The approach, referred to as the intrinsic complexity of language identification, employs notions of``weak'' and``strong'' reduction between learnable classes of languages. The intrinsic complexity of several classes is considered and the results agree with the intuitive difficulty of learning these classes. Several complete classes are shown for both the reductions and it is also established that the weak and strong reductions are distinct. An interesting result is that the self-referential class of Wiehagen in which the minimal element of every language is a grammar for the language and the class of pattern languages introduced by Angluin are equivalent in the strong sense. This study has been influenced by a similar treatment of function identification by Freivalds, Kinber, and Smith. ]

Machine learning of limit programs (i.e., pro-N. Shapiro. Review of "Limiting recursion" by E.M. Gold and "Trial and error predicates and the solution to a problem of Mostowski" by H. Putnam. Journal of Symbolic Logic,

Recently, rich subclasses of elementary formal systems (EFS) have been shown to be identifiable in the limit from only positive data. Examples of these classes are Angluin's pattern languages, unions of pattern languages by Wright and Shinohara, and classes of languages definable by length-bounded elementary formal systems studied by Shinohara. The present paper employs two distinct bodies of abstract studies in the inductive inference literature to analyze the learnability of these concrete classes. The first approach, introduced by Freivalds and Smith, uses constructive ordinals to bound the number of mind changes. ω denotes the first limit ordinal. An ordinal mind