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Incremental concept learning for bounded data mining
 Information and Computation
, 1999
"... Important re nements of concept learning in the limit from positive data considerably restricting the accessibility of input data are studied. Let c be any concept; every in nite sequence of elements exhausting c is called positive presentation of c. In all learning models considered the learning ma ..."
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Cited by 39 (29 self)
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Important re nements of concept learning in the limit from positive data considerably restricting the accessibility of input data are studied. Let c be any concept; every in nite sequence of elements exhausting c is called positive presentation of c. In all learning models considered the learning machine computes a sequence of hypotheses about the target concept from a positive presentation of it. With iterative learning, the learning machine, in making a conjecture, has access to its previous conjecture and the latest data item coming in. In kbounded examplememory inference (k is a priori xed) the learner is allowed to access, in making a conjecture, its previous hypothesis, its memory of up to k data items it has already seen, and the next element coming in. In the case of kfeedback identi cation, the learning machine, in making a conjecture, has access to its previous conjecture, the latest data item coming in, and, on the basis of this information, it can compute k items and query the database of previous data to nd out, for each of the k items, whether or not it is in the database (k is again a priori xed). In all cases, the sequence of conjectures has to converge to a hypothesis
Elementary formal systems, intrinsic complexity, and procrastination
 Information and Computation
, 1997
"... 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 lengthbounded e ..."
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Cited by 13 (6 self)
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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 lengthbounded 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 change bound of ω means that identification can be carried out by a learner that after examining some element(s) of the language announces an upper bound on the number of mind changes it will make before converging; a bound of ω · 2 means that the learner reserves the right to revise this upper bound once; a bound of ω · 3 means the learner reserves the right to revise this upper bound twice, and so on. A bound of ω 2 means that identification can be carried out by a learner that announces an upper bound on the number of times it may revise its conjectured upper bound on the number of mind changes. It is shown in the present paper that the ordinal mind change complexity for identification of languages formed by unions of up to n pattern languages is ω n. It is
On a generalized notion of mistake bounds
 Information and Computation
"... This paper proposes the use of constructive ordinals as mistake bounds in the online learning model. This approach elegantly generalizes the applicability of the online mistake bound model to learnability analysis of very expressive concept classes like pattern languages, unions of pattern languag ..."
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Cited by 2 (2 self)
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This paper proposes the use of constructive ordinals as mistake bounds in the online learning model. This approach elegantly generalizes the applicability of the online mistake bound model to learnability analysis of very expressive concept classes like pattern languages, unions of pattern languages, elementary formal systems, and minimal models of logic programs. The main result in the paper shows that the topological property of effective finite bounded thickness is a sufficient condition for online learnability with a certain ordinal mistake bound. An interesting characterization of the online learning model is shown in terms of the identification in the limit framework. It is established that the classes of languages learnable in the online model with a mistake bound of α are exactly the same as the classes of languages learnable in the limit from both positive and negative data by a Popperian, consistent learner with a mind change bound of α. This result nicely builds a bridge between the two models. 1
Synthesis of Recursive Functions with Interdependent Parameters
, 1998
"... . We present a methodology for the inductive synthesis of recursive functions based on the theoretical framework of contextfree tree grammars. The synthesis task is splitted into two parts: First, a small set of positive input/output examples is transformed into an "initial program" by means of h ..."
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Cited by 1 (1 self)
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. We present a methodology for the inductive synthesis of recursive functions based on the theoretical framework of contextfree tree grammars. The synthesis task is splitted into two parts: First, a small set of positive input/output examples is transformed into an "initial program" by means of heuristic search; second, the initial program is generalized to a recursive function. In this paper we concentrate on the second part of the synthesis task. We will describe our theoretical framework and propose an induction algorithm. The algorithm works without information about the number of parameters which might occur in the initial program. Subterms which change in a regular way are identified as parameters together with a substitution. It is possible to deal with substitutions which are interdependent between the parameters. Thereby we can infer a greater class of recursive functions than standard generalizationton techniques. Keywords. inductive program synthesis, grammatical...
Inductive Program Synthesis as Induction of ContextFree Tree Grammars
, 1998
"... . We present an application of grammar induction in the domain of inductive program synthesis. Synthesis of recursive programs from input/output examples involves the solution of two subproblems: transforming examples into straightforward programs and folding straightforward programs into (a set of) ..."
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. We present an application of grammar induction in the domain of inductive program synthesis. Synthesis of recursive programs from input/output examples involves the solution of two subproblems: transforming examples into straightforward programs and folding straightforward programs into (a set of) recursive equations. In this paper we focus on the second part of the synthesis problem, which corresponds to program synthesis from multiple traces or programming by demonstration. Instead of the original framework of synthesis of LISP functions and the currently prominent framework of inductive logic programming, we take a more general view coveringboth research areas: the synthesis of recursive program schemes. We show that this problem corresponds to the problem of inferring a contextfree tree grammar from a single noisefree positive example and provide a synthesis method. While our method does (of course) not solve the synthesis problem for the unrestricted set of recursive program s...