On the complexity analysis of static analyses

  • Authors:
  • David McAllester

  • Affiliations:
  • AutoReason.com, New Providence, NJ

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 2002

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Abstract

This paper argues that for many algorithms, and static analysis algorithms in particular, bottom-up logic program presentations are clearer and simpler to analyze, for both correctness and complexity, than classical pseudo-code presentations. The main technical contribution consists of two theorems which allow, in many cases, the asymptotic running time of a bottom-up logic program to be determined by inspection. It is well known that a datalog program runs in O(nk) time where k is the largest number of free variables in any single rule. The theorems given here are significantly more refined. A variety of algorithms are presented and analyzed as examples.