Myhill graphs also generalize to the SLk case. The k-factors, however, cannot simply denote edges. Rather the string σ_{1}σ_{2} ....... σ_{k-1}σ_{k} asserts, in essence, that if we have just scanned σ_{1}σ_{2} ....... σ_{k-1} the next symbol is permitted to be σ_{k}. The question of whether a given symbol causes the computation to reject or not depends on the preceding k - 1 symbols. Thus, we will take the vertices of the graph to be labeled with strings of length less than or equal to k - 1 over Σ plus one vertex labeled ‘x' and one labeled ‘x'.
We can interpret a k-factor σ_{1}σ_{2} σ_{k-1}σ_{k}, then, as denoting an edge between the node labeled σ_{1}σ_{2} ........σ_{k-1} and that labeled σ_{2}.......σ_{k} (the last k - 1 symbols of the string obtained by adding σk to the end of σ_{1}σ_{2} ........σ_{k-1}). While the symbol responsible for the transition along an edge can be determined by looking at the last symbol of the label of the node the edge leads to, for clarity we will label the edges with that symbol as well.
Each of the factors of form xσ_{2} ........ σ_{k} will be interpreted as a path from the vertex labeled x through the vertices labeled with successive pre?xes of σ_{2} ........ σ_{k}, to the vertex labeled σ_{2} ........ σ_{k} with the edges labeled σ_{2}, . . . , σ_{k} in sequence. Those of the form σ_{1} ...... σ_{k-1}x will be interpreted as an edge from the vertex labeled σ_{1} ...... σ_{k-1} to that labeled ‘x', with the edge labeled ‘ε'.
Finally, those of the form xσ_{1}.......σ_{ix}, for 0 ≤ i < k - 1, (where the substring σ_{1} ........ σ_{i} may be empty) will be interpreted as a path through vertices labeled with successive pre?xes of σ σ (possibly no intermediate vertices) from the vertex labeled ‘x' to that labeled ‘x', with the edges labeled with σ_{1}, . . . , σ_{i} (possibly ε) in sequence.