| Title | : | Hazard-free Circuits : Power & Limitations |
| Speaker | : | Balagopal Komarath (Saarland University, Germany) |
| Details | : | Wed, 6 Dec, 2017 3:00 PM @ A M Turing Hall |
| Abstract: | : | 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. |
