Lower bounds for sorting of sums

In parameterized complexity, each problem instance comes with a parameter k, and a parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance to an instance with size ...

Preprocessing (data reduction or kernelization) to reduce instance size is one of the most commonly deployed heuristics in the implementation practice to tackle computationally hard problems. However, a systematic theoretical study of them has remained ...

We give a general transformation which turns polynomialsize Frege proofs to subexponential-size AC⁰-Frege proofs. This indicates that proving exponential lower bounds for AC⁰-Frege is hard, since it is a longstanding open problem to prove super-...