The Othello game on an n × n board is PSPACE-complete

Iwata, Shigeki; Kasai, Takeshi

doi:10.1016/0304-3975(94)90131-7

Cited by 61 publications

(20 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In complexity theory, as will be seen in the next section, we can study differences in complexity between general mathematical problems. So, for example, we can know that the general problem of finding the best strategy for the game reversi (Othello) is less complex than that of chess (Iwata and Kasai 1994;Fraenkel and Lichtenstein 1981).…”

Section: What Is Cognitive Complexity?mentioning

confidence: 99%

Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving

Pantsar

2019

Erkenn

View full text Add to dashboard Cite

Following Marr's famous three-level distinction between explanations in cognitive science, it is often accepted that focus on modeling cognitive tasks should be on the computational level rather than the algorithmic level. When it comes to mathematical problem solving, this approach suggests that the complexity of the task of solving a problem can be characterized by the computational complexity of that problem. In this paper, I argue that human cognizers use heuristic and didactic tools and thus engage in cognitive processes that make their problem solving algorithms computationally suboptimal, in contrast with the optimal algorithms studied in the computational approach. Therefore, in order to accurately model the human cognitive tasks involved in mathematical problem solving, we need to expand our methodology to also include aspects relevant to the algorithmic level. This allows us to study algorithms that are cognitively optimal for human problem solvers. Since problem solving methods are not universal, I propose that they should be studied in the framework of enculturation, which can explain the expected cultural variance in the humanly optimal algorithms. While mathematical problem solving is used as the case study, the considerations in this paper concern modeling of cognitive tasks in general.

show abstract

Section: What Is Cognitive Complexity?mentioning

confidence: 99%

Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving

Pantsar

2019

Erkenn

View full text Add to dashboard Cite

show abstract

“…As for games on the (n × n)-extension of a square grid, Othello [7], Rush Hour [4], and Amazons [5] are known to be PSPACE-hard.…”

Section: Generalized Chat Noirmentioning

confidence: 99%

Generalized Chat Noir is PSPACE-Complete

Iwamoto

Mukai

Sumida

et al. 2013

IEICE Trans. Inf. & Syst.

View full text Add to dashboard Cite

SUMMARYWe study the computational complexity of the following two-player game. The instance is a graph G = (V, E), an initial vertex s ∈ V, and a target set T ⊆ V. A "cat" is initially placed on s. Player 1 chooses a vertex in the graph and removes it and its incident edges from the graph. Player 2 moves the cat from the current vertex to one of the adjacent vertices. Players 1 and 2 alternate removing a vertex and moving the cat, respectively. The game continues until either the cat reaches a vertex of T or the cat cannot be moved. Player 1 wins if and only if the cat cannot be moved before it reaches a vertex of T . It is shown that deciding whether player 1 has a forced win on the game on G is PSPACE-complete.

show abstract

“…Generalized to an n × n board with an arbitrary initial configuration, the game is clearly in PSPACE because only n 2 − 4 moves can be made. Furthermore, Iwata and Kasai [IK94] proved that the game is PSPACEcomplete.…”

Section: Othello (Reversi)mentioning

confidence: 99%

Playing games with algorithms: Algorithmic combinatorial game theory

Demaine¹,

Hearn²

2009

Games of No Chance 3

View full text Add to dashboard Cite

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we begin with general background in Combinatorial Game Theory, which analyzes ideal play in perfect-information games, and Constraint Logic, which provides a framework for showing hardness. Then we survey results about the complexity of determining ideal play in these games, and the related problems of solving puzzles, in terms of both polynomial-time algorithms and computational intractability results. Our review of background and survey of algorithmic results are by no means complete, but should serve as a useful primer.

show abstract

The Othello game on an n × n board is PSPACE-complete

Cited by 61 publications

References 9 publications

Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving

Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving

Generalized Chat Noir is PSPACE-Complete

Playing games with algorithms: Algorithmic combinatorial game theory

Contact Info

Product

Resources

About