In HTML, a & marks the begin of a reference, either of a character reference or of an entity reference. From that point on, the parser expects either a # denoting a character reference, or an entity name denoting an entity reference, both followed by a ;. That’s the normal behavior.
But if the reference name or just the reference opening & is followed by a white space or other delimiters like ", ', <, >, &, the ending ; and even a reference to represent a plain, & can be omitted:
<p title="&">foo & bar</p>
<p title="&">foo & bar</p>
<p title="&">foo & bar</p>
Only in these cases can the ending ; or even the reference itself be omitted (at least in HTML 4). I think HTML 5 requires the ending ;.
But the specification recommends to always use a reference like the character reference & or the entity reference & to avoid confusion:
Authors should use "&" (ASCII decimal 38) instead of "&" to avoid confusion with the beginning of a character reference (entity reference open delimiter). Authors should also use "&" in attribute values since character references are allowed within CDATA attribute values.
for example, I don't think this "validator" is correct.