Re-entrant polygon

A re-entrant, or concave polygon is one in which at least one interior angle is more than 180 degrees (i.e. a reflex angle). A polygon is re-entrant or concave if there exist two points within the polygon which cannot be connected by a straight line which lies within the polygon.

Some authors use "re-entrant" as a synonym for "concave" [1].

Some authors define "re-entrant" polygons as polygons with a boundary that "touches" itself. [2] [3] [4] All such polygons are concave, but not all concave polygons have a boundary that "touches" itself.

Some authors define "re-entrant" polygons as polygons with a boundary that intersects itself. [5] All such polygons are concave, but not all polygons that have a boundary that "touches" itself (much less all concave polygons) have a boundary that intersects itself.

Are they valid definitions?