this paper we assume, without loss of generality, that for all oe ` ø , [M(oe) 6=?] ) [M(ø) 6=?].

A team of learning machines is essentially a multiset of learning machines.

An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) generates a sequence of decision procedures defining the family. F. Stephan’s model of noisy data is employed, in which, roughly, correct data crops up infinitely often, and incorrect data only finitely often. Studied, then, is the synthesis from indices for r.e. classes and for indexed families of languages of various kinds of noise-tolerant language-learners for the corresponding classes or families indexed. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The proofs of most of the positive results yield, as pleasant corollaries, strict subset-principle or tell-tale style characterizations for the noise-tolerant learnability of the corresponding classes or families indexed. 1

The present paper studies the problem of when a team of learning machines can be aggregated into a single learning machine without any loss in learning power. The main results concern aggregation ratios for vacillatory identification of languages from texts. For a positiveinteger n,amachine is said to TxtFex n -identify a language L just in case the machine converges to up to n grammars for L on any text for L.For such identification criteria, the aggregation ratio is derived for the n = 2 case. It is shown that the collection of languages that can be TxtFex 2 identified by teams with success ratio greater than 5=6 are the same as those collections of languages that can be TxtFex 2 - identified by a single machine. It is also established that 5=6 is indeed the cut-off point by showing that there are collections of languages that can be TxtFex 2 -identified bya team employing 6 machines, at least 5 of which are required to be successful, but cannot be TxtFex 2 -identified byany single machine. Additionally, aggregation ratios are also derived for finite identification of languages from positive data and for numerous criteria involving language learning from both positive and negative data.

An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) generates a sequence of decision procedures defining the family. F. Stephan's model of noisy data is employed, in which, roughly, correct data crops up infinitely often, and incorrect data only finitely often. In a completely computable universe, all data sequences, even noisy ones, are computable. New to the present paper is the restriction that noisy data sequences be, nonetheless, computable! Studied, then, is the synthesis from indices for r.e. classes and for indexed families of languages of various kinds of noise-tolerant language-learners for the corresponding classes or families indexed, where the noisy input data sequences are restricted to being computable. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The main positive result is surpris...

Georgetown University Let A be a set of functions. A classifier for A is a way of telling, given a function f, if f is in A. We will define this notion formally. We will then modify our definition in three ways: (1) Allow the classifier to ask questions to an oracle A (thus increasing the classifiers computational power). (2) Allow the classifier to ask questions about f (thus increasing the classifiers information access). (3) Restrict the number of times the classifier can change its mind (thus decreasing the classifiers information access). By varying these parameters we will gain a better understanding of the contrast between computational power and informational access. We have determined exactly (1) which sets are classifiable (Theorem 3.6), (2) which sets are classifiable with queries to some oracle

Abstract not found

Abstract not found

this paper we address the issue of how to compose teams. While this endeavor may sound like it belongs in the realm of psychology, it turns out that there are some interesting things that can be formally proved us- This work was facilitated by an international agreement under NSF Grant 9119540.

Abstract. A classical learning problem in Inductive Inference consists of identifying each function of a given class of recursive functions from a finite number of its output values. Uniform learning is concerned with the design of single programs solving infinitely many classical learning problems. For that purpose the program reads a description of an identification problem and is supposed to construct a technique for solving the particular problem. As can be proved, uniform solvability of collections of solvable identification problems is rather influenced by the description of the problems than by the particular problems themselves. When prescribing a specific inference criterion (for example learning in the limit), a clever choice of descriptions allows uniform solvability of all solvable problems, whereas even the most simple classes of recursive functions are not uniformly learnable without restricting the set of possible descriptions. Furthermore the influence of the hypothesis spaces on uniform learnability is analysed. 1