Download Algorithmic Learning Theory: 14th International Conference, by Thomas Eiter (auth.), Ricard Gavaldá, Klaus P. Jantke, Eiji PDF

By Thomas Eiter (auth.), Ricard Gavaldá, Klaus P. Jantke, Eiji Takimoto (eds.)

This booklet constitutes the refereed complaints of the 14th foreign convention on Algorithmic studying idea, ALT 2003, held in Sapporo, Japan in October 2003.

The 19 revised complete papers offered including 2 invited papers and abstracts of three invited talks have been conscientiously reviewed and chosen from 37 submissions. The papers are geared up in topical sections on inductive inference, studying and knowledge extraction, studying with queries, studying with non-linear optimization, studying from random examples, and on-line prediction.

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Additional info for Algorithmic Learning Theory: 14th International Conference, ALT 2003, Sapporo, Japan, October 17-19, 2003. Proceedings

Example text

Assume ψ and (di )i∈N fulfil the conditions above. Let d be a recursive numbering corresponding to the limiting r. e. family (di )i∈N . By Property 2, Pψ is Ex -complete; thus, by Theorem 1, there exists a dense r. e. subclass C ⊆ Pψ . Let ψ be a one-one, recursive numbering with Pψ = C, in particular Pψ is dense. It remains to find a limiting r. e. family (di )i∈N of descriptions in D such that ψi ∈ Rdi for all i ∈ N. For that purpose define a corresponding numbering d . Given i, n ∈ N, define di (n) as follows.

Sn−1 )τsm (y) − 1. Now D1 is UEx -reducible to {d} via Θ, Ξ; details are omitted. 3. Example 4 moreover serves for proving the completeness of other sets, if Lemma 5 – an immediate consequence of Lemma 3 – is applied. Lemma 5 Let D1 , D2 ∈ UEx . If D1 is UEx -complete and UEx -reducible to D2 , then D2 is UEx -complete. Lemma 5 and Example 4 simplify the proofs of further examples, finally revealing that there are indeed UEx -complete description sets representing singleton recursive cores only.

Definition 3 [15,8] Let Θ be a total function operating on functions. Θ is a recursive operator, iff for all functions f, g and all numbers n, y ∈ N: 1. if f ⊆ g, then Θ(f ) ⊆ Θ(g); 2. if Θ(f )(n) = y, then Θ(f )(n) = y for some initial segment f ⊆ f ; 3. if f is finite, then one can effectively (in f ) enumerate Θ(f ). Reducing a class C1 of functions to a class C2 of functions requires two operators: the first one maps C1 into C2 ; the second maps any admissible sequence for a mapped function in C2 to an admissible sequence for the associated original function in C1 .

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