Ikenmeyer, Christian, Komarath, Balagopal and Saurabh, Nitin
(2021)
Karchmer-Wigderson Games for Hazard-free Computation.
[Preprint]
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2107.05128v1.pdf - Submitted version Download (373kB) | Preview |
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.
| Item Type: | Preprint |
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| Additional Information: | 34 pages, To appear in ITCS 2023 |
| Uncontrolled Keywords: | cs.CC, cs.CC, cs.DM, F.1 |
| Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 02 Aug 2021 08:31 |
| Last Modified: | 18 Jan 2023 21:34 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3131722 |
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