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TitleTowards the automated synthesis of a Gr\"obner bases algorithm.
Author(s) Bruno Buchberger
TypeArticle in Journal
Abstract We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates that, with this approach, the automated synthesis of the author?s Gröbner bases algorithm is possible. Still, significant technical work will be necessary to improve the current theorem provers, in particular the ones in the Theorema system, so that the road map can be transformed into a completely computerized process.
ISSN1578-7303
URL https://eudml.org/doc/41036
LanguageEnglish
JournalRACSAM, Rev. R. Acad. Cienc. Exactas F
Volume98
Number1-2
Pages65--75
PublisherReal Academia de Ciencias, Madrid
Year2004
Edition0
Translation No
Refereed No
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