Hilchos Shofar, Succah v’Lulav 4:7

A succah without a roof is invalid. This refers to a succah whose walls are connected like those of a hut, or a succah whose side is against a wall. If a succah has a roof, even if it’s only a handbreadth wide (about three inches), or if one lifts the side of the succah that is near the wall a handbreadth above the ground, it is valid. A round succah whose circumference is sufficient to contain a square seven handbreadths by seven handbreadths (about 21”x21”) is valid even though it has no corners.

Hilchos Shofar, Succah v’Lulav 4:8

If a person lays schach over a portico that has projections, it is valid regardless of whether these projections can be seen from inside the structure but not outside, or from outside the structure but not inside.