  A language $L$ over an alphabet $\Sigma$ is prefix-convex if, for any words
$x,y,z\in\Sigma^*$, whenever $x$ and $xyz$ are in $L$, then so is $xy$.
Prefix-convex languages include right-ideal, prefix-closed, and prefix-free
languages. We study complexity properties of prefix-convex regular languages.
In particular, we find the quotient/state complexity of boolean operations,
product (concatenation), star, and reversal, the size of the syntactic
semigroup, and the quotient complexity of atoms. For binary operations we use
arguments with different alphabets when appropriate; this leads to higher tight
upper bounds than those obtained with equal alphabets. We exhibit most complex
prefix-convex languages that meet the complexity bounds for all the measures
listed above.
