P versus NP

Determine whether the deterministic polynomial-time complexity class P equals the nondeterministic polynomial-time class NP; equivalently, determine whether every decision problem whose solutions can be verified in polynomial time by a deterministic Turing machine can also be solved in polynomial time by a deterministic Turing machine.

Background

The paper motivates its satirical ‘doomsday algorithm’ by invoking the long-standing open problem of whether P equals NP. Class P consists of decision problems solvable in deterministic polynomial time, while NP consists of decision problems for which a proposed solution can be verified in deterministic polynomial time. It is straightforward that P is contained in NP, but it is unknown whether this containment is strict.

This open problem underpins the paper’s premise: by leveraging Many-Worlds-style post-selection via a ‘doomsday channel,’ the authors argue that surviving observers would experience NP problems as solvable in polynomial time. The authors reference the P vs NP question explicitly to frame their construction against a foundational unresolved issue in computational complexity.