Deciding the Winner of an Arbitrary Finite Poset Game Is PSPACE-Complete
نویسنده
چکیده
A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the poset loses. Polynomial time algorithms exist for certain restricted classes of poset games, such as the game of Nim. However, until recently the complexity of arbitrary finite poset games was only known to exist somewhere between NC and PSPACE. We resolve this discrepancy by showing that deciding the winner of an arbitrary finite poset game is PSPACE-complete. To this end, we give an explicit reduction from Node Kayles, a PSPACE-complete game in which players vie to chose an independent set in a graph.
منابع مشابه
On Two-Level Poset Games
We consider the complexity of determining the winner of a finite, two-level poset game. This is a natural question, as it has been shown recently that determining the winner of a finite, three-level poset game is PSPACE-complete. We give a simple formula allowing one to compute the status of a type of two-level poset game that we call parity-uniform. This class includes significantly more easil...
متن کاملPSPACE-completeness of the Weighted Poset Game
Poset game, which includes some famous games. e.g., Nim and Chomp as sub-games, is an important two-player impartial combinatorial game. The rule of the game is as follows: For a given poset (partial ordered set), each player intern chooses an element and the selected element and it’s descendants (elements succeeding it) are all removed from the poset. A player who choose the last element is th...
متن کاملLocal Model Checking Games for Fixed Point Logic with Chop
The logic considered in this paper is FLC, fixed point logic with chop. It is an extension of modal μ-calculus Lμ that is capable of defining non-regular properties which makes it interesting for verification purposes. Its model checking problem over finite transition systems is PSPACE-hard. We define games that characterise FLC’s model checking problem over arbitrary transition systems. Over f...
متن کاملOn the Computational Complexity of the Domination Game
The domination game is played on an arbitrary graph $G$ by two players, Dominator and Staller. It is known that verifying whether the game domination number of a graph is bounded by a given integer $k$ is PSPACE-complete. On the other hand, it is showed in this paper that the problem can be solved for a graph $G$ in $mathcal O(Delta(G)cdot |V(G)|^k)$ time. In the special case when $k=3$ and the...
متن کاملReachability Switching Games
In this paper, we study the problem of deciding the winner of reachability switching games. These games provide deterministic analogues of Markovian systems. We study zero-, one-, and two-player variants of these games. We show that the zero-player case is NL-hard, the one-player case is NP-complete, and that the two-player case is PSPACE-hard and in EXPTIME. In the oneand two-player cases, the...
متن کامل