I have been reading the book Tata (Tree Automata Techniques and Applications), and there is a sentence I have read thousands of times, yet still don't quite understand.
In the beginning of Chapter 2, the authors want to show that regular string languages and regular tree languages have very much in common:
We shall see [...] that many properties and concepts on regular word languages smoothly generalize to regular tree languages, and that algebraic characterizations of regular languages do exist for tree languages.
The sentence I don't understand then follows:
Actually, this is not surprising since tree languages can be seen as word languages on an infinite alphabet of contexts.
How can I see a tree language as a word language on an infinite alphabet of contexts?