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Results tagged with automata-theory
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user 176424
6
votes
0
answers
112
views
Are "germ" automata studied?
I've been exploring the idea of a nondeterministic continuous automaton based on germs:
Two functions $f,g: \mathbb{R} \to S$ have the same right germ at $x$ if there is some interval $[x,a)$ on which …
- 429
0
votes
0
answers
65
views
First-order logics expressively equivalent to the computable languages
There is a really nice theorem that the subsets of $(\Sigma^*, =_{el}, \preceq, (S_a)_{a \in \Sigma})$ definable in first-order logic are exactly the regular sets.
Where:
$\Sigma^*$ is the set of fin …
- 429
4
votes
0
answers
163
views
Corollaries of Kleene's Theorem (Regular Languages)
Kleene's theorem that finite automata (specifically, nondeterministic) are expressively equivalent to regular expressions seems to be a powerful and not immediately obvious tool for untangling the sta …
- 429
2
votes
0
answers
99
views
Name for the theory of words with equal length, prefix, successors
I've worked with this theory for a while, but I've never been quite sure what to call it:
$$(\Sigma^*, =_{el}, \preceq, (S_a)_{a \in \Sigma})$$
Where
$\Sigma^*$ is the set of finite words on finite a …
- 429