By Thomas Eiter (auth.), Ricard Gavaldá, Klaus P. Jantke, Eiji Takimoto (eds.)
This ebook constitutes the refereed lawsuits of the 14th foreign convention on Algorithmic studying concept, ALT 2003, held in Sapporo, Japan in October 2003.
The 19 revised complete papers provided including 2 invited papers and abstracts of three invited talks have been rigorously reviewed and chosen from 37 submissions. The papers are prepared 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.
Read or Download Algorithmic Learning Theory: 14th International Conference, ALT 2003, Sapporo, Japan, October 17-19, 2003. Proceedings PDF
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Extra info for Algorithmic Learning Theory: 14th International Conference, ALT 2003, Sapporo, Japan, October 17-19, 2003. Proceedings
Let j ∈ N be minimal such that ψi =n ψj . (* Note that, for all but ﬁnitely many n, the index j will be the minimal ψ-program of ψi . *) Return di (n) := dj (n). (* lim(di ) = dj , for j minimal with ψi = ψj . *) Finally, let di be given by the limit of the function di , in case a limit exists. Fix i ∈ N. Then there is a minimal j with ψi = ψj . By deﬁnition, the limit di of di exists and di = dj ∈ D. Moreover, as ψj ∈ Rdj , the function ψi is in Rdi . As ψ and (di )i∈N allow us to apply Theorem 7, the set D is UEx -complete.
Let D ∈ UEx . 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.
L. Pitt, Inductive Inference, DFAs and Computational Complexity, in “Proc. 2nd Int. P. ), Lecture Notes in Artiﬁcial Intelligence, Vol. 397, pp. 18–44, Springer-Verlag, Berlin, 1989. 32. R. Reischuk and T. Zeugmann, Learning One- Variable Pattern Languages in Linear Average Time, in “Proc. 11th Annual Conference on Computational Learning Theory - COLT’98,” July 24th - 26th, Madison, pp. 198–208, ACM Press 1998. 33. R. Reischuk and T. Zeugmann, A Complete and Tight Average-Case Analysis of Learning Monomials, in “Proc.