On brain plasticity and regular expressions

In the construction above, every new word I learn requires linearly more storage space for the regular expression or the NFA: they just keep growing as a learn new words. This is in analogy to Merzenich’s second language observation: second languages occupy brain regions distinct from the native tongue’s. You’ll also note that the computational complexity (i.e., the effort for “speaking” the language) of this construction is terrible; a naive implementation of the union of regular expressions is:

Just like the human brain, regular expressions can do better.

First, we can turn the non-deterministic automaton into a deterministic automaton (DFA), sketched to the left. You’ll note that the DFA has fewer states, and that this reduction is achieved by sharing some of the DFA states (here: C, A) across different words. In terms of the natural language analogy, this could be interpreted as a given set of neurons recognizing similar sounds across different languages.

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