We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in
Applying
Sequence mappability is an important task in genome resequencing. In the (
We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in
Applying
We consider the problem of covering multiple submodular constraints. Given a finite ground set
Let us fix a prime
In a Merlin–Arthur proof system, the proof verifier (Arthur) accepts valid proofs (from Merlin) with probability 1, and rejects invalid proofs with probability arbitrarily close to 1. The running time of such a system is defined to be the length of Merlin’s proof plus the running time of Arthur. We provide new Merlin–Arthur proof systems for some key problems in fine-grained complexity. In several cases our proof systems have optimal running time. Our main results include: Certifying that a list of Counting the number of Computing the All-Pairs Shortest Distances matrix for an Certifying that an Certifying a Quantified Boolean Formula is true can be done in Merlin–Arthur time
Due to the centrality of these problems in fine-grained complexity, our results have consequences for many other problems of interest. For example, our work implies that certifying there is no Subset Sum solution to
A classical parking function of length