Foundations of Information Technologies

- FIT 2009 -

June 14-27, 2009, Novi Sad

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  Conway Games, coalgebraically

Furio Honsell
 

 

Abstract

 

Using coalgebraic methods, we show how to extend Conway's original theory of games to include infinite games (hypergames). We take the view that a play which goes on forever is a draw, and hence rather than focussing on winning strategies, we focus on non-losing strategies. Infinite games are a fruitful metaphor for non-terminating processes,  Conway's sum of games being similar to shuffling. Hypergames have a rather interesting theory, already in the case of  generalized Nim. The theory of hypergames generalizes Conway's theory rather smoothly,  but significantly. We will indicate a number of intriguing directions for future work, and  we will briefly compare infinite games with other notions of games used in computer science.
 

 

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