Mind change complexity of learning logic programs

Jain, Sanjay; Sharma, Arun

doi:10.1016/s0304-3975(01)00084-6

Cited by 13 publications

(3 citation statements)

References 39 publications

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“…Only much later, did Berardi and de'Liguoro [9] generalize the concept of 1-backtracking to the more general n-backtracking for any n ∈ N. It was a major conceptual advancement. Their definition is inspired by Gold's learning theory [19,23] and by the Berardi-Coquand-Hayashi [11] notion of n-backtracking game -an alternative to Coquand and Hyland-Ong games up to now only partially explored. However, it was not at all obvious how to formulate a notion of n-backtracking strategy in Coquand and Hyland-Ong games as well, which is what they did.…”

Section: Berardi-de'liguoro Backtracking Level Of a Strategymentioning

confidence: 99%

Game Semantics and the Geometry of Backtracking: A New Complexity Analysis of Interaction

Aschieri¹

2017

J. symb. log.

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We present abstract complexity results about Coquand and Hyland-Ong game semantics, that will lead to new bounds on the length of first-order cut-elimination, normalization, interaction between expansion trees and any other dialogical process game semantics can model and apply to. In particular, we provide a novel method to bound the length of interactions between visible strategies and to measure precisely the tower of exponentials defining the worst-case complexity. Our study improves the old estimates on average by several exponentials.

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Section: Berardi-de'liguoro Backtracking Level Of a Strategymentioning

confidence: 99%

Game Semantics and the Geometry of Backtracking: A New Complexity Analysis of Interaction

Aschieri¹

2017

J. symb. log.

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“…Another application is the design of SMC-optimal learners for logic programs. For example, Jain and Sharma have examined classes of logic programs that can be learned with bounded mind changes using explorer trees [14]. Do explorer trees lead to mind change optimal learning algorithms?…”

Section: Summary and Future Workmentioning

confidence: 99%

Mind change efficient learning

Luo

2006

Information and Computation

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“…After incorporating ordinals into the on-line learning model, we derive a sufficient condition for a class of languages to have a mistake bound of the form ω × n, where n is a natural number. This condition is established in terms of the concept class satisfying the topological property of effective finite bounded thickness [Ang80b,Wri89,Shi91,JS99].…”

Section: Introductionmentioning

confidence: 99%

On a Generalized Notion of Mistake Bounds

Jain

Sharma

2001

Information and Computation

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This paper proposes the use of constructive ordinals as mistake bounds in the on-line learning model. This approach elegantly generalizes the applicability of the on-line 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 on-line learnability with a certain ordinal mistake bound. An interesting characterization of the on-line learning model is shown in terms of the identification in the limit framework. It is established that the classes of languages learnable in the on-line 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.

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Mind change complexity of learning logic programs

Abstract: The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts.

Cited by 13 publications

References 39 publications

Game Semantics and the Geometry of Backtracking: A New Complexity Analysis of Interaction

Game Semantics and the Geometry of Backtracking: A New Complexity Analysis of Interaction

Mind change efficient learning

On a Generalized Notion of Mistake Bounds

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