| Autor: |
Ikenmeyer, Christian, Komarath, Balagopal, Lenzen, Christoph, Lysikov, Vladimir, Mokhov, Andrey, Sreenivasaiah, Karteek |
| Rok vydání: |
2017 |
| Předmět: |
|
| Zdroj: |
J. ACM 66(4), Article 25 (2019) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1145/3320123 |
| Popis: |
The problem of constructing hazard-free Boolean circuits dates back to the 1940s and is an important problem in circuit design. Our main lower-bound result unconditionally shows the existence of functions whose circuit complexity is polynomially bounded while every hazard-free implementation is provably of exponential size. Previous lower bounds on the hazard-free complexity were only valid for depth 2 circuits. The same proof method yields that every subcubic implementation of Boolean matrix multiplication must have hazards. These results follow from a crucial structural insight: Hazard-free complexity is a natural generalization of monotone complexity to all (not necessarily monotone) Boolean functions. Thus, we can apply known monotone complexity lower bounds to find lower bounds on the hazard-free complexity. We also lift these methods from the monotone setting to prove exponential hazard-free complexity lower bounds for non-monotone functions. As our main upper-bound result we show how to efficiently convert a Boolean circuit into a bounded-bit hazard-free circuit with only a polynomially large blow-up in the number of gates. Previously, the best known method yielded exponentially large circuits in the worst case, so our algorithm gives an exponential improvement. As a side result we establish the NP-completeness of several hazard detection problems. |
| Databáze: |
arXiv |
| Externí odkaz: |
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