Are you merely looking for unicity of the last character?
In that case, you may mean a property such as:
- the regular expression ends with a character
xc for some expression
x and character
- the language described by the regular expression ends with a character
Lc for some regular language
L and character
They are different properties:
acc* meets 2 but not 1.
Or are you looking for a stronger property, that must also apply elsewhere in the expression?
In that case, you may be looking for determinism. Determinism is the property of never
having to backtrack and retry while trying to parse (match) a string. It is usually defined assuming parsing from left to right, so it applies to unicity of prefixes rather than suffixes; and it is usually defined for finite automata or context-free grammars rather than regular expressions (but not always - see, e.g., this paper about deterministic regular expressions).
In that case, you may be looking for a property such as:
- the reverse of the regular expression is deterministic
Here, the reverse is the regular expression obtained by swapping all concatenation arguments, e.g. the reverses of
I don't know a name for any of these properties.