On the complexity of hazard-Free circuits
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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.
Original language | English |
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Title of host publication | STOC 2018 : Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing |
Number of pages | 14 |
Place of Publication | New York |
Publisher | Association for Computing Machinery |
Publication date | 20 Jun 2018 |
Pages | 253-266 |
ISBN (Electronic) | 978-1-4503-5559-9 |
DOIs | |
Publication status | Published - 20 Jun 2018 |
Externally published | Yes |
Event | 50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, United States Duration: 25 Jun 2018 → 29 Jun 2018 |
Conference
Conference | 50th Annual ACM Symposium on Theory of Computing, STOC 2018 |
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Land | United States |
By | Los Angeles |
Periode | 25/06/2018 → 29/06/2018 |
Sponsor | ACM Special Interest Group on Algorithms and Computation Theory (SIGACT) |
Series | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN | 0737-8017 |
- Boolean circuits, Computational complexity, Hazards, Monotone circuits
Research areas
ID: 232711583