Multi-sample anti-aliasing is a popular technique for reducing geometric aliasing (jagged edges) and is supported in all modern graphics processors. With multi-sampling anti-aliasing, visibility and depth are sampled more than once per pixel, while shading is done only once per pixel per primitive. Although this significantly reduces the appearance of jagged edges around object boundaries, the ...

This paper describes a method for merging behavior specifications modeled by transition systems. Given two behavior specifications B1 and B2, Merge(B1, B2) defines a new behavior specification that extends B1 and B2. Moreover, provided that a necessary and sufficient condition holds, Merge(B1, B2) is a cyclic extension of B1 and B2. In other words, Merge(B1, B2) extends B1 and B2, and any cycli...

This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent spaces. DMTs combine both $$\pi _0$$ and $$H_n$$ information into single data structure that distinguishes filtrations homology cannot distinguish alone. Three variants on DMTs, which emphasize category theory, representation theory persistence barcodes, respectively, offer different advantages in terms of co...

In this paper, we study merge trees induced by a discrete Morse function on tree. Given function, provide method to constructing an tree and define new notion of equivalence functions based the We then relate matching number certain invariant Finally, count that can be star graph characterize

heap objects are represented by a tuple (h, hc, r) ∈ H×HC×R. H is the set of allocation sites, HC includes all heap contexts, and R = {R, NR} is a flag that indicates whether an object is most-recent (R) or non-most-recent (NR). If an abstract object is most-recent, it corresponds to a single concrete object, thus its fields can be strongly updated and should be tracked flow-sensitively. Nonmos...

This paper describes the concept of workflow merge and methods for merging business processes. We grouped merges in four categories according to the type of merge: sequential, parallel, conditional, and iterative, and describe the corresponding algorithms for performing these operations. We give results that allow us to determine whether a merge operation is sound. It is shown that to avoid inv...