By Topic

Modeling and Isomorphisms of Positional Board Games

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Sergio Antoy ; Istituto per la Matematica Applicata, Via L.B. Alberti 4, 1-16132 Genova, Italy.

A model is proposed for a class of two-person games based on the occupation of positions on a board. Well-known games that can be rephrased within or with the help of the model are, for example, tic-tac-toe, qubic, go-moku, hex, and connect-four. The model is formulated in terms of a composite algebraic structure called board. A notion of board isomorphism is defined, a few concepts fundamental for positional board game playing are identified, and necessary and sufficient conditions for establishing the isomorphism of two boards are proved. The formalism of the model provides criteria for the description and analysis of a board that are more abstract than its physical characteristics such as size and dimensionality. The application of the isomorphism results to the implementation of more general and efficient software modules for game playing is discussed. Related work is briefly outlined and compared.

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:PAMI-9 ,  Issue: 5 )