Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages

Abstract

A language L over an alphabet Σ is suffix-convex if, for any words x,y,z∈Σ∗, 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.