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TitleTowards the Automated Synthesis of a Gröbner Bases Algorithm
Author(s) Bruno Buchberger
TypeArticle in Journal
AbstractWe 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.
Keywordssynthesis method,lazy thinking,theorem invention,algorithm invention
Length11
File
LanguageEnglish
JournalRACSAM (Review of the Spanish Royal Academy of Sciences)
Volume98
Pages65 - 75
Year2004
Translation No
Refereed Yes
Organization Johannes Kepler University Linz
Institution RISC (Research Institute for Symbolic Computation)
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