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oai:drops-oai.dagstuhl.de:17577 2024-03-06T10:59:57Z ddc:004 open_access

Karchmer-Wigderson Games for Hazard-Free Computation Ikenmeyer, Christian Komarath, Balagopal Saurabh, Nitin Hazard-free computation monotone computation Karchmer-Wigderson games communication complexity lower bounds 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Christian Ikenmeyer and Balagopal Komarath and Nitin Saurabh 2023 Is Part Of LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2023.74 urn:nbn:de:0030-drops-175775 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.74 eng https://creativecommons.org/licenses/by/4.0/legalcode