2 Citations
Edge Hop: A Framework to Show NP-Hardness of Combinatorial Games
- Computer ScienceElectron. Colloquium Comput. Complex.
- 2018
It is shown that the decision question whether the marked token can reach the goal node is NP-complete and several gadgets are constructed to show a reduction via Directed Hamiltonian cycles.
References
SHOWING 1-10 OF 56 REFERENCES
Phutball Endgames are Hard
- MathematicsArXiv
- 2000
It is shown that, in John Conway’s board game Phutball, it is NPcomplete to determine whether the current player has a move that immediately wins the game.
GO Is Polynomial-Space Hard
- MathematicsJACM
- 1980
It is proved that GO is Pspace hard by reducing a Pspace-complete set, TQBF, to a game called generalized geography, then to a planar version of that game, and finally to GO.
The complexity of checkers on an N × N board
- Mathematics19th Annual Symposium on Foundations of Computer Science (sfcs 1978)
- 1978
Under certain reasonable assumptions about the "drawing rule" in force, the problem of whether a specified player can force a win against best play by his opponent is shown to be PSPACE-hard.
Generalized Amazons is PSPACE-Complete
- Computer ScienceIJCAI
- 2005
This paper presents two proofs for the PSPACE-completeness of the generalized version of the full game Amazons, a perfect information board game with simple rules and large branching factors.
Gradual Abstract Proof Search
- Computer ScienceJ. Int. Comput. Games Assoc.
- 2002
GAPS is a new 2-player search technique that has been used to prove that 11x11 Phutball is a win for the first player in 25 plies or less, and that 6x6 Atari-Go with a crosscut in the center is awin for the second player in 15 plied or less.
Rush Hour is PSPACE-complete
- Computer Science
- 2011
In this report we give a formal definition of the sliding block puzzle Rush Hour and we report on the proof showing that Rush Hour is PSPACE-complete from “The nondeterministic constraint logic model…
One-Dimensional Phutball
- Physics
- 2002
The case of a restricted version of one-dimensional phutball called Oddish Phutball is solved by presenting an explicit strategy in terms of a potential function.
A Combinatorial Problem Which Is Complete in Polynomial Space
- MathematicsJACM
- 1976
It is shown that determining who wins such a game if each player plays perfectly is very hard; this result suggests that the theory of combinational games is difficult.
N by N Checkers is Exptime Complete
- Computer Science, MathematicsSIAM J. Comput.
- 1984
The question of whether a particular player can force a win from a given position and also the question of what is the best move in agiven position are considered.