Abstract
The usual approach to the synthesis of algorithms for the solution of problems in combinatorial mathematics consists of two steps.
1 — Description: the problem is embedded in a general structure which is rich enough to permit a mathematical modelling of the problem.
2 — Solution: the problem is solved by means of techniques "as simple as possible", with respect to some given notion of complexity.
We give a formalization of this approach in the framework of category theory, which is general enough to get rid of unessential details. In particular such a framework will be provided by the category of ordered complete Σ-algebras, and we will describe the relation between description and solution by means of a variant of so called "Mezei-Wright like results" [10], relating the concept of least fixed point to that of a suitable natural transformation between functors.
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© 1977 Springer-Verlag Berlin Heidelberg
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Bertoni, A., Mauri, G., Torelli, M. (1977). An algebraic approach to problem solution and problem semantics. In: Gruska, J. (eds) Mathematical Foundations of Computer Science 1977. MFCS 1977. Lecture Notes in Computer Science, vol 53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08353-7_143
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DOI: https://doi.org/10.1007/3-540-08353-7_143
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08353-5
Online ISBN: 978-3-540-37285-1
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