Mathematical problems, rewriting, normal forms. (Problemi matematici, riscritture, forme normali.) (Italian. English summary)

Archimede 61, No. 3, 143-149 (2009).

Author’s summary: This paper refers to a general notion of one-person games. As a particular case, rewriting systems are dealt with. The main theoretical features are introduced and some examples are presented and discussed. Some of these examples are related to topics in mathematics teaching. In particular, the notion of “normal form" is discussed. Among the examples, taken from literature, there are “The Greek Urn" and the “Chameleon Island". The former is discussed following additive structures of integers modulo $m$. In the latter, we explain why, in the presented version, it is not possible to reach a normal form.