Lifschitz and Turner introduced the notion of the splitting set and provided a method to divide a logic program into two parts. They showed that the task of computing the answer sets of the program can be converted into the tasks of computing the answer sets of these parts. However, the empty set and the set of all atoms are the only two splitting sets for many programs, then these programs can...

This paper introduces Index-Set Splitting (ISS), a technique that splits a loop containing several conditional statements into several loops with less complex control flow. Contrary to the classic loop unswitching technique, ISS splits loops when the conditional is loop variant. ISS uses an Index Sub-range Tree (IST) to identify the structure of the conditionals in the loop and to select which ...

The aim of a multi-mode resource-constrained project scheduling problem (MRCPSP) is to assign resource(s) with the restricted capacity to an execution mode of activities by considering relationship constraints, to achieve pre-determined objective(s). These goals vary with managers or decision makers of any organization who should determine suitable objective(s) considering organization strategi...

We apply the Piecewise Constant Level Set Method (PCLSM) to a multiphase motion problem, especially the pure mean curvature motion. We use one level set function to represent multiple regions, and by associating an energy functional which consists of surface tension (proportional to length), we formulate a variational approach for the mean curvature motion problem. Some operator-splitting schem...

Adleman wrote the first paper that demonstrated that DNA (DeoxyriboNucleic Acid) strands could be applied for dealing with solutions of the NP-complete Hamiltonian path problem (HPP). Lipton wrote the second paper that showed that the Adleman techniques could also be used to solve the NP-complete satisfiability (SAT) problem (the first NP-complete problem). Adleman and his co-authors proposed s...

Splitting off a pair su; sv of edges in a graph G means the operation that deletes su and sv and adds a new edge uv. Given a graph G = (V + s;E) which is k-edge-connected (k 2) between vertices of V and a specified subset R V , first we consider the problem of finding a longest possible sequence of disjoint pairs (splittings) of edges sx; sy, x; y 2 R which can be split off preserving k-edge-co...

The stationary set splitting game is a game of perfect information of length ω1 between two players, unsplit and split, in which unsplit chooses stationarily many countable ordinals and split tries to continuously divide them into two stationary pieces. We show that it is possible in ZFC to force a winning strategy for either player, or for neither. This gives a new counterexample to Σ2 maximal...

Consider the problem of minimizing, over a polyhedral set, the composition of an affine mapping with a strictly convex essentially smooth function. A general result on the linear convergence of descent methods for solving this problem is presented. By applying this result, the linear convergence of both the gradient projection algorithm of Goldstein and Levitin and Polyak, and a matrix splittin...