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COMPLEXITY OF SHORT GENERATING FUNCTIONS

Part of: Theory of computing

Published online by Cambridge University Press:  14 February 2018

DANNY NGUYEN  and
IGOR PAK
DANNY NGUYEN
Affiliation:
Department of Mathematics, University of California, Los Angeles, USA; ldnguyen@math.ucla.edu, pak@math.ucla.edu
IGOR PAK
Affiliation:
Department of Mathematics, University of California, Los Angeles, USA; ldnguyen@math.ucla.edu, pak@math.ucla.edu

Abstract

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We give complexity analysis for the class of short generating functions. Assuming #P$\not \subseteq$FP/poly, we show that this class is not closed under taking many intersections, unions or projections of generating functions, in the sense that these operations can increase the bit length of coefficients of generating functions by a super-polynomial factor. We also prove that truncated theta functions are hard for this class.

MSC classification

Primary: 68Q17: Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
Secondary: 68Q15: Complexity classes (hierarchies, relations among complexity classes, etc.)
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 6 , 2018 , e1
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2018

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