Jumping Automata over Infinite Words

Jumping automata are finite that read their input in a non-consecutive manner, disregarding the order of letters word. We introduce and study jumping over infinite words. Unlike setting words, which has been well studied, for words it is not clear how can be reordered. To this end, we consider three semantics: word some so no letter overlooked, permute windows given size k, an existentially-quantified bound. expressiveness, closure properties algorithmic these models.