  A language $L$ over an alphabet $\Sigma$ is suffix-convex if, for any words
$x,y,z\in\Sigma^*$, whenever $z$ and $xyz$ are in $L$, then so is $yz$.
Suffix-convex languages include three special cases: left-ideal, suffix-closed,
and suffix-free languages. We examine complexity properties of these three
special classes of suffix-convex regular languages. In particular, we study the
quotient/state complexity of boolean operations, product (concatenation), star,
and reversal on these languages, as well as the size of their syntactic
semigroups, and the quotient complexity of their atoms.
