Invited Talk by Dr. Balagopal Komarath on On the complexity of hazard-free circuits

Title: On the complexity of hazard-free circuits
Speaker:Dr. Balagopal Komarath, Saarland University
Host Faculty:  Dr. Karteek sreenivasaiah
Room No: A-220, academic block A.
Time: 14:30
 

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.

Speaker Bio:

Dr. Balagopal Komarath is a postdoc researcher in the complexity group at Saarland University, Germany. He obtained his PhD from IITM in 2015. He research interests are in circuit complexity and algorithms.

Dates: 
Tuesday, December 12, 2017 - 14:30