Computation of partial automata through span composition

In this paper a way to have structures with partiality in its internal structure in a categorical approach is presented and, with this, a category of partial graphs $\mathcal{G}r_{p}$ is given and partial automata are constructed from $\mathcal{G}r_{p}$. With a simple categorical operation, computations of partial automata are given and can be seen as a part of the structure of partial automata.