Abstract
In computable mathematics, there are known definitions of computable numbers, computable metric spaces, computable compact sets, and computable functions. A traditional definition of a computable function, however, covers only continuous functions. In many applications (e.g., in phase transitions), physical phenomena are described by discontinuous or multi-valued functions (a.k.a. constraints). In this paper, we provide a physics-motivated definition of computable discontinuous and multi-valued functions, and we analyze properties of this definition.
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References
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Acknowledgements
This work was supported in part by NSF grants HRD-1242122 and DUE-0926721, by NIH Grants 1 T36 GM078000-01 and 1R43TR000173-01, and by an ONR grant N62909-12-1-7039.
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Ceberio, M., Kosheleva, O., Kreinovich, V. (2018). Towards a Physically Meaningful Definition of Computable Discontinuous and Multi-valued Functions (Constraints). In: Ceberio, M., Kreinovich, V. (eds) Constraint Programming and Decision Making: Theory and Applications. Studies in Systems, Decision and Control, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-319-61753-4_7
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DOI: https://doi.org/10.1007/978-3-319-61753-4_7
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