Permutation automaton

A permutation automaton (or p-automaton) is an automaton such that each input permutes the set of states. In other words, a permutation automaton is a reset-free deterministic finite automaton.

Formally, an automaton $A=(S,I,\delta ,s_{0},F)$ is a permutation automaton if and only if:

$\forall s_{i},s_{j}\in S\ \forall a\in I\ \delta (s_{i},a)=\delta (s_{j},a)\implies s_{i}=s_{j}$

A language is p-regular if it is accepted by a permutation automaton.