Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2007) 2007
DOI: 10.1109/synasc.2007.55
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Abstract: In the context of a scheme based exploration model proposed by Bruno Buchberger, we investigate the idea of decomposition, applied in the exploration of natural numbers. The free decomposition problem (i.e. whether an element can always be decomposed with respect to an operation) can be arbitrarily difficult, and we illustrate this in the theory of natural numbers. We consider a restriction, the decomposition in domains with a well-founded partial ordering: we introduce the notions of irreducible elements, red… Show more

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Cited by 4 publications
(4 citation statements)
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“…The approach is further refined in (Buchberger, 2004), where a scheme-based model for theory exploration in the Theorema system is introduced. This is also applied on natural numbers in (Craciun and Hodorog, 2007). Theory exploration consists of two processes: top-down and bottom-up, which are followed in parallel.…”
Section: Additional Certification Of the Synthesized Algorithmsmentioning
confidence: 99%
“…The approach is further refined in (Buchberger, 2004), where a scheme-based model for theory exploration in the Theorema system is introduced. This is also applied on natural numbers in (Craciun and Hodorog, 2007). Theory exploration consists of two processes: top-down and bottom-up, which are followed in parallel.…”
Section: Additional Certification Of the Synthesized Algorithmsmentioning
confidence: 99%
“…The scheme-based model for theory exploration in the Theorema system, introduced in [4] by Bruno Buchberger, is applied on natural numbers in [6]. The set theory is described in [16], and [15].…”
Section: B Related Workmentioning
confidence: 99%
“…However, the user needs to perform all schematic substitutions manually as Theorema does not instantiate the schemes automatically from a set of terms. The user also needs to conduct the proof obligations interactively [10]. Another important difference is that ensuring the soundness of definitions is left to the user in Theorema.…”
Section: Related Workmentioning
confidence: 99%
“…A case study of mathematical theory exploration is described in [10] for the theory of natural numbers using the scheme-based approach. However, apart from this paper there is, to our knowledge, no other case study of scheme-based mathematical theory exploration.…”
Section: Introductionmentioning
confidence: 99%