Finite-State Complexity and the Size of Transducers
Cristian S. Calude, Kai Salomaa, Tania Roblot · Electronic Proceedings in Theoretical Computer Science · 2010
Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our main result, we show that the state-size hierarchy with respect to a standard encoding is infinite. We consider also hierarchies yielded by more general computable encodings.