In computational complexity theory, P and NP are two classes of problems. P is the class of decision problems that a deterministic Turing machine can solve in polynomial time. In useful terms, any ...

The subset-sum problem is one of the most frequently occurring NP (nondeterministic, polynomial-time)-complete) problems. It asks whether a subset of numbers in a set of positive integers adds up ...

The subset sum problem involves determining whether a specific subset of numbers can sum to a given target. By mapping this problem onto their photonic processor, the researchers can encode the ...

In this paper we study generic complexity of undecidable problems. It turns out that some classical undecidable problems are, in fact, strongly undecidable, i.e., they are undecidable on every ...

We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with k prime factors for every k between 3 and 19,565,220. These computations ...

Light propagates in a three-dimensional photonic circuit to solve the subset sum problem. The image of the reconfigurable photonic processor is based on the research presented. As technology advances, ...