Scaling, Renormalization, and Universality in Combinatorial Games: The Geometry of Chomp

2007 ◽  
pp. 200-207
Author(s):  
Eric J. Friedman ◽  
Adam Scott Landsberg
Keyword(s):  
Combinatorial Games

Combinatorial Games

2008 ◽  
Author(s):  
Jozsef Beck
Keyword(s):  
Combinatorial Games

scholarly journals Combinatorial games modeling seki in GO

2014 ◽  
Vol 329 ◽  
pp. 19-32
Author(s):  
Andrey Gol’berg ◽  
Vladimir Gurvich ◽  
Diogo Andrade ◽  
Konrad Borys ◽  
Gabor Rudolf
Keyword(s):  
Combinatorial Games

scholarly journals Automatic Synthesis of Generalized Winning Strategies of Impartial Combinatorial Games Using SMT Solvers

2020 ◽  
Author(s):  
Kaisheng Wu ◽  
Liangda Fang ◽  
Liping Xiong ◽  
Zhao-Rong Lai ◽  
Yong Qiao ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Game Theory ◽  
Experimental Results ◽  
Combinatorial Games ◽  
Logical Framework ◽  
Automatic Synthesis ◽  
Integer Arithmetic ◽  
Smt Solvers ◽  
Winning Strategies

Strategy representation and reasoning has recently received much attention in artificial intelligence. Impartial combinatorial games (ICGs) are a type of elementary and fundamental games in game theory. One of the challenging problems of ICGs is to construct winning strategies, particularly, generalized winning strategies for possibly infinitely many instances of ICGs. In this paper, we investigate synthesizing generalized winning strategies for ICGs. To this end, we first propose a logical framework to formalize ICGs based on the linear integer arithmetic fragment of numeric part of PDDL. We then propose an approach to generating the winning formula that exactly captures the states in which the player can force to win. Furthermore, we compute winning strategies for ICGs based on the winning formula. Experimental results on several games demonstrate the effectiveness of our approach.

scholarly journals Combinatorial games with a pass: A dynamical systems approach

2011 ◽  
Vol 21 (4) ◽  
pp. 043108 ◽  
Author(s):  
Rebecca E. Morrison ◽  
Eric J. Friedman ◽  
Adam S. Landsberg
Keyword(s):  
Dynamical Systems ◽  
Systems Approach ◽  
Combinatorial Games
Sign in / Sign up

Export Citation Format

Share Document