Karchmer-Wigderson games for hazard-free computation

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dc.contributor.author Ikenmeyer, Christian
dc.contributor.author Komarath, Balagopal
dc.contributor.author Saurabh, Nitin
dc.date.accessioned 2012-09-26T07:22:32Z
dc.date.available 2012-09-26T07:22:32Z
dc.date.issued 2021-07
dc.identifier.citation Ikenmeyer, Christian; Komarath, Balagopal and Saurabh, Nitin, "Karchmer-Wigderson games for hazard-free computation", arXiv, Cornell University Library, DOI: arXiv:2107.05128, Jul. 2021. en_US
dc.identifier.uri http://arxiv.org/abs/2107.05128
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/6656
dc.description.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 significant step towards establishing hazard-free computation as an independent missing link between Boolean complexity and monotone complexity.
dc.description.statementofresponsibility by Christian Ikenmeyer, Balagopal Komarath and Nitin Saurabh
dc.language.iso en_US en_US
dc.publisher Cornell University Library en_US
dc.title Karchmer-Wigderson games for hazard-free computation en_US
dc.type Pre-Print en_US
dc.relation.journal arXiv

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