کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
402409 676936 2012 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
XT Domineering: A new combinatorial game
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
XT Domineering: A new combinatorial game
چکیده انگلیسی

This paper introduces a new combinatorial game, named XT Domineering, together with its mathematical analysis. XT Domineering is modified from the Domineering game in which 1 × 2 or 2 × 1 dominos are allowed to be placed on empty squares in an m × n board. This new game allows a player to place a 1 × 1 domino on an empty square s while unable to place a 1 × 2 or 2 × 1 domino in the connected group of empty squares that includes s. After modifying the rule, each position in the game becomes an infinitesimal. This paper calculates the game values of all sub-graphs of 3 × 3 squares and shows that each sub-graph of 3 × 3 squares is a linear combination of 8 elementary infinitesimals. These pre-stored game values can be viewed as a knowledge base for playing XT Domineering. Instead of searching the whole game trees, a simple rule for determining the optimal outcome of any sum of these positions is presented.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Knowledge-Based Systems - Volume 34, October 2012, Pages 55–63
نویسندگان
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