Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
434284 | Theoretical Computer Science | 2014 | 13 Pages |
Abstract
We show that a self-generated set of combinatorial games, S, may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question “Is there a set which will give a non-distributive but modular lattice?” appears. A useful necessary condition for the existence of a finite non-distributive modular L(S)L(S) is proved. We show the existence of S such that L(S)L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Alda Carvalho, Carlos Pereira dos Santos, Cátia Dias, Francisco Coelho, João Pedro Neto, Richard Nowakowski, Sandra Vinagre,