Computational Complexity Analysis of the Grandfather Paradox as an NP-Complete Problem

The Grandfather Paradox, a classic problem in philosophy and theoretical physics, is analyzed through the lens of computational complexity theory. By modeling the paradox as a Constraint Satisfaction Problem (CSP) and demonstrating its equivalence to the Boolean Satisfiability Problem (SAT), we argue that finding a self-consistent history in a system with causal loops is an NP-complete problem. We generalize the problem, showing that as the number of variables increases, the search space grows exponentially, reinforcing the inherent exponential nature of “causal loop” problems in NP. This report establishes the Grandfather Paradox as a quintessential example of an NP problem that is likely intractable in polynomial time, supporting the hypothesis that P $\neq$ NP and suggesting that such problems may not conceal a polynomial-time solution.