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An iterative method for linear decomposition of index generating functions

  • S. HodžićEmail author
  • E. Pasalic
  • A. Chattopadhyay
Article
  • 12 Downloads

Abstract

Various methods for reducing hardware implementation cost of incompletely specified index generating functions have been proposed lately. Considering the methods based on linear decomposition, for the first time in this work, we provide necessary and sufficient conditions which describe the linear decomposition of these functions in general. These conditions are derived using the concept of functional degeneracy, and we show that the problem of linear decomposition can be translated into the problem of constructing suitable coordinate Boolean functions (which represent the generating functions) such that the linear decomposition is possible. In this context, we propose several design methods of such Boolean functions and furthermore we employ one particular design method to derive a new iterative semi-deterministic algorithm for linear decomposition. In addition, we provide a general result which describes all incompletely specified index generating functions for which the linear decomposition is (not) possible. Consequently, our results indicate that the functional degeneracy is a promising approach in derivation of new deterministic-like algorithms for linear decomposition of incompletely specified index generating functions.

Keywords

(Incompletely specified) index generating functions Linear decomposition Linear injective mappings 

Mathematics Subject Classification (2010)

06E30 65T50 

Notes

Acknowledgments

Samir Hodžić is supported in part by the Slovenian Research Agency (research program P3-0384 and Young Researchers Grant). Enes Pasalic is partly supported by the Slovenian Research Agency (research program P3-0384 and research project J1-9108). Also, the first two authors gratefully acknowledge the European Commission for funding the InnoRenew CoE project (Grant Agreement no. 739574) under the Horizon2020 Widespread-Teaming program and the Republic of Slovenia (Investment funding of the Republic of Slovenia and the European Union of the European regional Development Fund). Anupam Chattopadhyay will like to acknowledge Tsutomu Sasao for helpful discussions related to the complexity of index generation functions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.FAMNITUniversity of PrimorskaKoperSlovenia
  2. 2.FAMNIT & IAMUniversity of PrimorskaKoperSlovenia
  3. 3.School of Computer Science and Engineering, College of EngineeringNTUSingaporeSingapore

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