## Robust Behaviourally Correct Learning (1998)

Venue: | Information and Computation |

Citations: | 4 - 2 self |

### BibTeX

@TECHREPORT{Jain98robustbehaviourally,

author = {Sanjay Jain},

title = {Robust Behaviourally Correct Learning},

institution = {Information and Computation},

year = {1998}

}

### OpenURL

### Abstract

Intuitively, a class of functions is robustly learnable if not only the class itself, but also all of the transformations of the class under natural transformations (such as via general recursive operators) are learnable. Fulk [Ful90] showed the existence of a non-trivial class which is robustly learnable under the criterion Ex. However, several of the hierarchies (such as the anomaly hierarchies for Ex and Bc) do not stand robustly. Fulk left open the question about whether Bc and Ex can be robustly separated. In this paper we resolve this question positively. 1

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(Show Context)
Citation Context ...ϕ p(i)) ⊆ {0, 1}. (E) For z ∈ {0, 1}, let Then {h0 i , h1i } �⊆ Ex(Mi). h z i (x) = � ϕp(i)(x), if ϕ p(i)(x)↓; z, otherwise. Proof. This proof is based on a modification of proof of Ex 1 − Ex �= ∅ in =-=[CS83]-=-. By operator recursion theorem [Cas74] there exists a recursive p such that ϕ p(i) may be defined in stages as follows. Initially, for x < i, ϕ p(i)(x) = 0, and ϕ p(i)(i) = 1. Let x0 = i + 1. Intuiti... |

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Citation Context ... partial computable function computed by program i in the ϕ-system. Note that in this paper all programs are interpreted with respect to the ϕ-system. We let Φ be an arbitrary Blum complexity measure =-=[Blu67]-=- associated with the acceptable programming system ϕ; many such measures exist for any acceptable programming system [Blu67]. For this paper, without loss of generality, we assume that Φi(x) ≥ x, for ... |

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(Show Context)
Citation Context ...let Then {h0 i , h1i } �⊆ Ex(Mi). h z i (x) = � ϕp(i)(x), if ϕ p(i)(x)↓; z, otherwise. Proof. This proof is based on a modification of proof of Ex 1 − Ex �= ∅ in [CS83]. By operator recursion theorem =-=[Cas74]-=- there exists a recursive p such that ϕ p(i) may be defined in stages as follows. Initially, for x < i, ϕ p(i)(x) = 0, and ϕ p(i)(i) = 1. Let x0 = i + 1. Intuitively, xs denotes the least x such that ... |

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Citation Context ... which can be Ex-identified, can also be Ex-identified using identification by enumeration. That is, every Ex-identifiable class is contained in a recursively enumerable class of functions. Bārzdiņˇs =-=[Bar71]-=- showed the above conjecture to be false using the “selfdescribing” class, SD = {f | f(0) is a program for f}. A machine can Ex-identify each function 1sf in SD by just outputting the program f(0). On... |