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

The final publication is available at Springer via http://dx.doi.org/10.1007%2F978-3-319-53733-7_12A 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.Natural Sciences and Engineering Research Council of Canada [grant No. OGP0000871