King Chasing Problem in Chinese Chess is NP-hard

TL;DR

The paper proves that determining a winning strategy in the king chasing problem in generalized Chinese Chess is NP-hard by reduction from 3-SAT.

Contribution

It establishes the computational complexity of the king chasing problem in Chinese Chess, showing it is NP-hard in generalized settings.

Findings

King chasing problem is NP-hard on n×n boards.

Reduction from 3-SAT demonstrates NP-hardness.

Implication for computational complexity of Chinese Chess strategies.

Abstract

We prove that king chasing problem in Chinese Chess is NP-hard when generalized to $n\times n$ boards. `King chasing' is a frequently-used strategy in Chinese Chess, which means that the player has to continuously check the opponent in every move until finally checkmating the opponent's king. The problem is to determine which player has a winning strategy in generalized Chinese Chess, under the constraints of king chasing. Obviously, it is a sub-problem of generalized Chinese Chess problem. We prove that king chasing problem in Chinese Chess is NP-hard by reducing from the classic NP-complete problem 3-SAT.