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An Algorithmic Characterization of Polynomial Functions over Z(pn)

Guha, Ashwin and Dukkipati, Ambedkar (2015) An Algorithmic Characterization of Polynomial Functions over Z(pn). In: ALGORITHMICA, 71 (1). pp. 201-218.

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Official URL: http://dx.doi.org/ 10.1007/s00453-013-9799-7


In this paper we consider polynomial representability of functions defined over , where p is a prime and n is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to determine whether a given function over is polynomially representable or not, and (ii) finds the polynomial if it is polynomially representable. The previous characterizations given by Kempner (Trans. Am. Math. Soc. 22(2):240-266, 1921) and Carlitz (Acta Arith. 9(1), 67-78, 1964) are existential in nature and only lead to an exhaustive search method, i.e. algorithm with complexity exponential in size of the input. Our characterization leads to an algorithm whose running time is linear in size of input. We also extend our result to the multivariate case.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 23 Mar 2015 10:05
Last Modified: 23 Mar 2015 10:05
URI: http://eprints.iisc.ac.in/id/eprint/51092

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