arXiv subjects
Publications and source records attributed to David Fernando Casas Torres.
We consider finite deterministic automata such that their alphabets consist of exactly one letter of defect 1 and a set of permutations of the state set. We study under which conditions such an automaton is completely reachable. We focus our attention on the case when the set of permutations generates a transitive imprimitive group.
Every function on a finite set defines an equivalence relation and, therefore, a partition called the kernel of the function. Automata such that every possible partition is the kernel of a word are called totally compatible. A characterization of such automata is given together with an algorithm to recognize them in polynomial running time with respect to the number of states.