Details

Autor(en) / Beteiligte

• Honsell, Furio
• Lenisa, Marina

Titel

Conway games, algebraically and coalgebraically

Ist Teil von

• Logical methods in computer science, 2011-09, Vol.7, Issue 3

Ort / Verlag

Logical Methods in Computer Science e.V

Erscheinungsjahr

2011

Link zum Volltext

Quelle

EZB Free E-Journals

Beschreibungen/Notizen

• Using coalgebraic methods, we extend Conway's theory of games to possibly non-terminating, i.e. non-wellfounded 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. Hypergames are a fruitful metaphor for non-terminating processes, Conway's sum being similar to shuffling. We develop a theory of hypergames, which extends in a non-trivial way Conway's theory; in particular, we generalize Conway's results on game determinacy and characterization of strategies. Hypergames have a rather interesting theory, already in the case of impartial hypergames, for which we give a compositional semantics, in terms of a generalized Grundy-Sprague function and a system of generalized Nim games. Equivalences and congruences on games and hypergames are discussed. We indicate a number of intriguing directions for future work. We briefly compare hypergames with other notions of games used in computer science.