The straight line complexity of small factorials and primorials

Klas Markström

The straight line complexity of small factorials and primorials

Computational Complexity 2014-12-16 v4 Discrete Mathematics Number Theory

Authors: Klas Markström

Abstract

In this paper we determine the straight-line complexity of $n!$ for $n\leq 22$ and give bounds for the complexities up to $n=46$ . In the same way we determine the straight-line complexity of the product of the first primes up to $p=31$ and gives bounds for $p\leq 43$ . Our results are based on an exhaustive computer search of the short length straight-line programs.

Keywords

straight-line complexity factorials primorials straight-line programs computer search computational complexity

Cite

@article{arxiv.1306.3091,
  title  = {The straight line complexity of small factorials and primorials},
  author = {Klas Markström},
  journal= {arXiv preprint arXiv:1306.3091},
  year   = {2014}
}

Comments

V4: Published version. Reformatted to journal format. Minor typos corrected. v3: Updated acknowledgments, improved some of the lower bounds after recomputing all data with a new program, corrected two incorrect lower bounds due a damaged datafile from the original 10 year old computation. V2: Corrected typos and a mistake in table 2

The straight line complexity of small factorials and primorials

Abstract

Keywords

Cite

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