License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2023.74
URN: urn:nbn:de:0030-drops-175775
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17577/
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Ikenmeyer, Christian ; Komarath, Balagopal ; Saurabh, Nitin

Karchmer-Wigderson Games for Hazard-Free Computation

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LIPIcs-ITCS-2023-74.pdf (0.8 MB)

Abstract

We present a Karchmer-Wigderson game to study the complexity of hazard-free formulas. This new game is both a generalization of the monotone Karchmer-Wigderson game and an analog of the classical Boolean Karchmer-Wigderson game. Therefore, it acts as a bridge between the existing monotone and general games.
Using this game, we prove hazard-free formula size and depth lower bounds that are provably stronger than those possible by the standard technique of transferring results from monotone complexity in a black-box fashion. For the multiplexer function we give (1) a hazard-free formula of optimal size and (2) an improved low-depth hazard-free formula of almost optimal size and (3) a hazard-free formula with alternation depth 2 that has optimal depth. We then use our optimal constructions to obtain an improved universal worst-case hazard-free formula size upper bound. We see our results as a step towards establishing hazard-free computation as an independent missing link between Boolean complexity and monotone complexity.

BibTeX - Entry

@InProceedings{ikenmeyer_et_al:LIPIcs.ITCS.2023.74,
  author =	{Ikenmeyer, Christian and Komarath, Balagopal and Saurabh, Nitin},
  title =	{{Karchmer-Wigderson Games for Hazard-Free Computation}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{74:1--74:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17577},
  URN =		{urn:nbn:de:0030-drops-175775},
  doi =		{10.4230/LIPIcs.ITCS.2023.74},
  annote =	{Keywords: Hazard-free computation, monotone computation, Karchmer-Wigderson games, communication complexity, lower bounds}
}

Keywords: Hazard-free computation, monotone computation, Karchmer-Wigderson games, communication complexity, lower bounds
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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