## Definition

Let $\CC$ be a collation system.

Let $\AA$ be an alphabet.

Suppose that for any two collations from $\CC$, $C$ and $C'$, in the alphabet $\AA$, it holds that:

If $C$ and $C'$ are indistinguishable, then $C = C'$.

Then $\CC$ has the unique readability property for $\AA$.

## Examples

It is clear that any word in natural language is uniquely readable: we are able to distinguish words if and only if they have a different letter at some position.

Some non-examples can help to illustrate the concept and its usefulness.

Non-examples come in two sorts: Ones where two placeholders cannot be distinguished, and ones where two symbols substituted for a placeholder cannot be distinguished.

As to the first, consider a coin with two identical sides. We consider a placeholder on each side, suitable for one letter.

Then if we write $A$ on one side and $B$ on the other, this cannot be distinguished from writing $B$ on the one side and $A$ on the other.

So since we cannot distinguish the two placeholders, there is no way of knowing whether we tried to express $AB$ or $BA$.

As to the second, consider writing down words of natural language without spaces.

Then we would have to guess whether $\mathsf {Iamnowhere}$ should be read as $\mathsf {I \, am \, now \, here}$ or as $\mathsf {I \, am \, nowhere}$.