Symbolic polynomial maximization over convex sets and its application to memory requirement estimation

  • Authors:

  • Philippe Clauss;Federico Javier Fernández;Diego Garbervetsky;Sven Verdoolaege

  • Affiliations:

  • Laboratory ICPS-LSIIT, Université Louis Pasteur, Illkirch, France;Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina;Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina;Leiden Institute of Advanced Computer Science, Universiteit Leiden, Leiden, The Netherlands and Department of Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium

  • Venue:
  • IEEE Transactions on Very Large Scale Integration (VLSI) Systems
  • Year:
  • 2009

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Abstract

Memory requirement estimation is an important issue in the development of embedded systems, since memory directly influences performance, cost and power consumption. It is therefore crucial to have tools that automatically compute accurate estimates of the memory requirements of programs to better control the development process and avoid some catastrophic execution exceptions. Many important memory issues can be expressed as the problem of maximizing a parametric polynomial defined over a parametric convex domain. Bernstein expansion is a technique that has been used to compute upper bounds on polynomials defined over intervals and parametric "boxes". In this paper, we propose an extension of this theory to more general parametric convex domains and illustrate its applicability to the resolution of memory issues with several application examples.