Geodesic
Computational complexity of the synthesis of composite models for Lipschitz-bounded functions
Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 103-110

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The paper is devoted to the analysis of computational complexity of the synthesis of composite models for Lipschitz-bounded surjective functions of single variable. Composite models are some function approximation methods based on approximating via composition of functions taken from a given set. In this paper, it is proved that the problem of building strictly optimal composite model for a target functions via a given set of functions is NP-complete. Methods that are capable to build a near-optimal composition model are discussed. Some of these methods can be realized as algorithms with the polynomial computational complexity but they have a limited application.
Keywords: function composition, composition models, NP-completeness, Lipschitz-bounded, computational complexity. 
@article{PDM_2014_3_a9,
     author = {I. S. Kalinnikov},
     title = {Computational complexity of the synthesis of composite models for {Lipschitz-bounded} functions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {103--110},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_3_a9/}
}
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I. S. Kalinnikov. Computational complexity of the synthesis of composite models for Lipschitz-bounded functions. Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 103-110. http://geodesic.mathdoc.fr/item/PDM_2014_3_a9/