Proper Prefix

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Definition

Proper Prefix

A proper prefix of a string $w$ is a prefix $p$ of $w$ with $|p|<|w|$.

Examples

Positive

Let $w=abc$. The proper prefixes of $w$ are $\epsilon$, $a$, and $ab$.

Negative

Let $w=abc$. The prefix $abc$ is not proper because $|abc|=|w|$. The string $abx$ is not a prefix at all.