Lower Runtime Bounds for Integer Programs

  • F. Frohn
  • M. Naaf
  • J. Hensel
  • M. Brockschmidt
  • J. GieslEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9706)


We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs. To this end, we construct symbolic representations of program executions using a framework for iterative, under-approximating program simplification. The core of this simplification is a method for (under-approximating) program acceleration based on recurrence solving and a variation of ranking functions. Afterwards, we deduce asymptotic lower bounds from the resulting simplified programs. We implemented our technique in our tool LoAT and show that it infers non-trivial lower bounds for a large number of examples.



We thank S. Genaim and J. Böker for discussions and comments.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • F. Frohn
    • 1
  • M. Naaf
    • 1
  • J. Hensel
    • 1
  • M. Brockschmidt
    • 2
  • J. Giesl
    • 1
    Email author
  1. 1.LuFG Informatik 2RWTH Aachen UniversityAachenGermany
  2. 2.Microsoft ResearchCambridgeUK

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