It is well known that lower bounds on circuits implies lower bounds on time complexity, just because circuits can efficiently simulate algorithms. By the continuous work started by Ryan Williams, we know that upper bounds on the algorithms can imply circuit lower bounds [1].Another connection between uniform and non-uniform complexities is that there exist algorithms that uses efficient circuits to gain a speed up. For example, first subquadratic algorithm for 3-sum [2] uses efficient decision trees. I'm looking for results in the direction I haven't discussed yet: can lower bounds for time complexity imply lower bounds for circuit complexity. It is worth mentioning that algorithms that uses efficient circuits are taking advantage of the actual constructions rather then pure existence.[1] Improving exhaustive search implies superpolynomial lower bounds. Ryan Williams.[2]Threesomes, Degenerates, and Love Triangles. Allan Grnlund, Seth Pettie
Non-uniform lower bounds from uniform
cc.complexity theory;circuit complexity