ECCC-Report TR21-100https://eccc.weizmann.ac.il/report/2021/100Comments and Revisions published for TR21-100en-usFri, 25 Nov 2022 13:42:39 +0200
Revision 1
| Karchmer-Wigderson Games for Hazard-free Computation |
Christian Ikenmeyer,
Balagopal Komarath,
Nitin Saurabh
https://eccc.weizmann.ac.il/report/2021/100#revision1We 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.Fri, 25 Nov 2022 13:42:39 +0200https://eccc.weizmann.ac.il/report/2021/100#revision1
Paper TR21-100
| Karchmer-Wigderson Games for Hazard-free Computation |
Christian Ikenmeyer,
Balagopal Komarath,
Nitin Saurabh
https://eccc.weizmann.ac.il/report/2021/100We 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.Mon, 12 Jul 2021 10:35:35 +0300https://eccc.weizmann.ac.il/report/2021/100