Journal article
On Learning Ring-Sum-Expansions
The problem of learning ring-sum-expansions from examples is studied. Ring-sum-expansions (RSE) are representations of Boolean functions over the base {#123;small infinum, (+), 1}#125;, which reflect arithmetic operations in GF(2). k-RSE is the class of ring-sum-expansions containing only monomials of length at most k:. term-RSE is the class of ring-sum-expansions having at most I: monomials.
It is shown that k-RSE, k>or=1, is learnable while k-term-RSE, k>2, is not learnable if RPnot=NP. Without using a complexity-theoretical hypothesis, it is proven that k-RSE, k>or=1, and k-term-RSE, k>or=2 cannot be learned from positive (negative) examples alone. However, if the restriction that the hypothesis which is output by the learning algorithm is also a k-RSE is suspended, then k-RSE is learnable from positive (negative) examples only.
Moreover, it is proved that 2-term-RSE is learnable by a conjunction of a 2-CNF and a 1-DNF. Finally the paper presents learning (on-line prediction) algorithms for k-RSE that are optimal with respect to the sample size (worst case mistake bound)
Language: | English |
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Year: | 1992 |
Pages: | 181-192 |
ISSN: | 10957111 and 00975397 |
Types: | Journal article |
DOI: | 10.1137/0221014 |
ORCIDs: | Fischer, Paul |