End-position equivalence

Two nonempty substrings have end-position equivalence when their sets of occurrence-ending positions in one fixed text are equal. This is the grouping used for states of a suffix automaton, with an additional initial state. In ababa, using one-based positions, b and ab both end at $\{2,4\}$, whereas a ends at $\{1,3,5\}$. Thus b and ab share a state despite their different lengths.^[ref]

Equality of ending sets ensures that appending the same character gives equal new ending sets whenever the extension occurs. This makes character transitions well defined. Within a class the represented strings are nested suffixes, one at every length in an interval; suffix links connect that interval to the next shorter class.