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

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.Comment: 20 pages, 11 figures, 1 table. arXiv admin note: text overlap with arXiv:1605.0669

The determination of derivative parameters for a monotonic rational quadratic interpolant

Explicit formulae are developed for determining the derivative parameters of a monotonic interpolation method of Gregory and Delbourgo (1982)

Filling polygonal holes with bicubic patches

Consider a bicubic rectangular patch complex which surrounds an n-sided hole in R3. Then the problem of filling the hole with n bicubic rectangular patches is studied

Polygonal patches of high order continuity

A polygonal patch is defined to fill an n-sided hole within a rectangular Ck patch framework. First a reparameterization of the surface around the hole is constructed, that is defined outside a regular polygon. The polygonal patch is an interpolant, defined inside the polygon, that matches this parameterization up to order k along the boundary. Some modifications and handles to control the shape of the patch are described