A map of update constraints in inductive inference

Kötzing, Timo; Palenta, Raphaela

doi:10.1016/j.tcs.2016.07.028

Cited by 12 publications

(39 citation statements)

References 19 publications

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“…The idea here is to, just as in the Ex W -case, mimic the given learner and to search for minimal locking sequences. Incorporating the result of Kötzing and Palenta (2016) that unrestricted Gold-style learners may be assumed total, we even get a stronger result.…”

Section: Casementioning

confidence: 88%

“…When studying language learning in the limit, there are certain properties of learner that are useful, e.g., if we can assume a learner to be total. Kötzing and Palenta (2016) and Kötzing et al (2017) study under which circumstances learners may be assumed to be total. Importantly, this is the case for explanatory Gold-style learners obeying delayable learning restrictions and for behaviorally correct learners obeying delayable restrictions.…”

Section: Normal Formsmentioning

confidence: 99%

“…Assume L can be learned by a TxtGEx Clearner h . By Kötzing and Palenta (2016), we can assume h ∈ R. Then, by ORT there exist indices e, p, q ∈ N such that…”

Section: Requiring C-indices As Outputmentioning

confidence: 99%

“…For the other, let h be a τ (δ)TxtGδ Ex C -learner, which can assumed to be total by Kötzing and Palenta (2016) and let L = τ (δ)TxtGδ Ex C (h) ∩ REC. We define, for each finite set D ⊆ N and t ∈ N,…”

Section: Casementioning

confidence: 99%

“…We show that there exists no learner h that TxtGEx C -learns L. To that end, assume there exists such a learner h , that is, L ⊆ TxtGEx C (h ). Without loss of generality, we may assume h to be total, as is shown in Kötzing and Palenta (2016).…”

Section: Syntactic Versus Semantic Convergence To C-indicesmentioning

confidence: 99%

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Learning Languages with Decidable Hypotheses

Berger¹,

Böther²,

Doskoč³

et al. 2020

Preprint

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In language learning in the limit, the most common type of hypothesis is to give an enumerator for a language. This so-called W -index allows for naming arbitrary computably enumerable languages, with the drawback that even the membership problem is undecidable. In this paper we use a different system which allows for naming arbitrary decidable languages, namely programs for characteristic functions (called C-indices). These indices have the drawback that it is now not decidable whether a given hypothesis is even a legal C-index.In this first analysis of learning with C-indices, we give a structured account of the learning power of various restrictions employing C-indices, also when compared with W -indices. We establish a hierarchy of learning power depending on whether C-indices are required (a) on all outputs; (b) only on outputs relevant for the class to be learned and (c) only in the limit as final, correct hypotheses. Furthermore, all these settings are weaker than learning with W -indices (even when restricted to classes of computable languages). We analyze all these questions also in relation to the mode of data presentation.Finally, we also ask about the relation of semantic versus syntactic convergence and derive the map of pairwise relations for these two kinds of convergence coupled with various forms of data presentation.

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Section: Casementioning

confidence: 88%

Section: Normal Formsmentioning

confidence: 99%

“…Assume L can be learned by a TxtGEx Clearner h . By Kötzing and Palenta (2016), we can assume h ∈ R. Then, by ORT there exist indices e, p, q ∈ N such that…”

Section: Requiring C-indices As Outputmentioning

confidence: 99%

Section: Casementioning

confidence: 99%

Section: Syntactic Versus Semantic Convergence To C-indicesmentioning

confidence: 99%

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