8
$\begingroup$

Apparently, the closest thing I've found would be normal number http://mathworld.wolfram.com/NormalNumber.html

But requiring that every finite words occurs is weaker than this property. So I'm wondering if there are any study on this topic.

My original goal is to find a criterion for a Büchi automaton not to recognize some infinite word like this. There's been a post here Proof that the $\omega$-language consisting of all words containing every finite word as a factor is not rational/regular , but there were no references to such a class of words.

Maybe all this is obvious to specialists, but I couldn't find anything with our universal friend google :)

Thank you!

$\endgroup$
  • 4
    $\begingroup$ I've used the term "universal" for this. $\endgroup$ – Joel David Hamkins May 18 '14 at 10:09
  • $\begingroup$ In dynamical systems, this property is called transitive. $\endgroup$ – Anthony Quas May 19 '14 at 3:04
7
$\begingroup$

One term that is used is disjunctive sequence. The linked article mentions some references, including an overview (from 1997) by Calude, Priese, and Staiger.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.