On the complexity of hazard-Free circuits

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

  • Christian Ikenmeyer
  • Lysikov, Vladimir
  • Balagopal Komarath
  • Andrey Mokhov
  • Christoph Lenzen
  • Karteek Sreenivasaiah

The problem of constructing hazard-free Boolean circuits dates back to the 1940s and is an important problem in circuit design. Our main lower-bound result unconditionally shows the existence of functions whose circuit complexity is polynomially bounded while every hazard-free implementation is provably of exponential size. Previous lower bounds on the hazard-free complexity were only valid for depth 2 circuits. The same proof method yields that every subcubic implementation of Boolean matrix multiplication must have hazards. These results follow from a crucial structural insight: Hazard-free complexity is a natural generalization of monotone complexity to all (not necessarily monotone) Boolean functions. Thus, we can apply known monotone complexity lower bounds to find lower bounds on the hazard-free complexity. We also lift these methods from the monotone setting to prove exponential hazard-free complexity lower bounds for non-monotone functions. As our main upper-bound result we show how to efficiently convert a Boolean circuit into a bounded-bit hazard-free circuit with only a polynomially large blow-up in the number of gates. Previously, the best known method yielded exponentially large circuits in the worst case, so our algorithm gives an exponential improvement. As a side result we establish the NP-completeness of several hazard detection problems.

Original languageEnglish
Title of host publicationSTOC 2018 : Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
Number of pages14
Place of PublicationNew York
PublisherAssociation for Computing Machinery
Publication date20 Jun 2018
Pages253-266
ISBN (Electronic)978-1-4503-5559-9
DOIs
Publication statusPublished - 20 Jun 2018
Externally publishedYes
Event50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, United States
Duration: 25 Jun 201829 Jun 2018

Conference

Conference50th Annual ACM Symposium on Theory of Computing, STOC 2018
LandUnited States
ByLos Angeles
Periode25/06/201829/06/2018
SponsorACM Special Interest Group on Algorithms and Computation Theory (SIGACT)
SeriesProceedings of the Annual ACM Symposium on Theory of Computing
ISSN0737-8017

    Research areas

  • Boolean circuits, Computational complexity, Hazards, Monotone circuits

ID: 232711583