Playing with Conway's Problem
Résumé
The centralizer of a language is the maximal language commuting with it. The question, raised by Conway in 1971, whether the centralizer of a rational language is always rational, recently received a lot of attention. In Kunc 2005, a strong negative answer to this problem was given by showing that even complete co-recursively enumerable centralizers exist for finite languages. Using a combinatorial game approach, we give here an incremental construction of rational languages embedding any recursive computation in their centralizers.