8

It seems it would depend on your particular model, in particular what information you have access to. From what I infer, you are thinking of the following model: you have a memory $m$, for instance of size $O(\log n)$. at each step, you read a new letter $a\in\Sigma$ of your stream, and you are allowed to modify your memory $m$ you then have to say whether ...


6

Here is a second, simpler and more general answer that was obtained after discussing with a3nm. Problem We fix a regular language $\mathcal{L}$ and we are interested in the following word problem. At start, we have an empty word and then we receive updates taking one of the following forms: Insert a letter at the beginning of the word Insert a letter at ...


6

Context Let $\mathcal{L}$ be a fixed regular language and let ($\mathcal{Q}, \Sigma, \delta, q_0, \mathcal{F})$ be an automaton recognizing $\mathcal{L}$. I will suppose in this post that we are working in the RAM model with cells of size logarithmic in the maximal size of the window, and that all the operations regarding the automaton are constant time. ...


4

This seems to be exactly the type of question studied by Moses Ganardi and coauthors in recent years. In particular this paper and this extension prove nice trichotomies.


Only top voted, non community-wiki answers of a minimum length are eligible