Ouch.
Look, no. Grammars look like "the key to the gates" because of the equivalence between grammars-language-automata etc. You can write up grammars for fully Turing-complete languages, or indeed context-free languages that allow you to declare Turing-complete automata.
You can create grammars that display infinite recursion with minimal effort:
A --> ε
A --> Aa
a --> <whatever you please>
So it's not like someone (cough, Chomsky) woke up one nice day and thought "blimey, I'll tell the world that grammars are a powerful tool for modelling hierarchical processes". It's that they
are.
We have used grammars in practice to model complex hierarchical processes- except it's only those processes that we already know how to model, because we came up with them ourselves, like the aforementioned Turing-complete ones.
The problems begin when we try to fit a process we hardly understand to a grammar. That is not a limitation of the tool itself. It's a limitation of our ability to use it.
Look, no. Grammars look like "the key to the gates" because of the equivalence between grammars-language-automata etc. You can write up grammars for fully Turing-complete languages, or indeed context-free languages that allow you to declare Turing-complete automata.
You can create grammars that display infinite recursion with minimal effort:
So it's not like someone (cough, Chomsky) woke up one nice day and thought "blimey, I'll tell the world that grammars are a powerful tool for modelling hierarchical processes". It's that they are.We have used grammars in practice to model complex hierarchical processes- except it's only those processes that we already know how to model, because we came up with them ourselves, like the aforementioned Turing-complete ones.
The problems begin when we try to fit a process we hardly understand to a grammar. That is not a limitation of the tool itself. It's a limitation of our ability to use it.