We introduce a framework allowing domain experts to manipulate computational terms in the interest of deriving better, more efficient implementations. It employs deductive reasoning to generate provably correct efficient implementations from a very high-level specification of an algorithm, and inductive constraint-based synthesis to improve automation. Semantic information is encoded into program terms through the use of refinement types.In this paper, we develop the technique in the context of a system called Bellmania that uses solver-aided tactics to derive parallel divide-and-conquer implementations of dynamic programming algorithms that have better locality and are significantly more efficient than traditional loop-based implementations. Bellmania includes a high-level language for specifying dynamic programming algorithms and a calculus that facilitates gradual transformation of these specifications into efficient implementations. These transformations formalize the divide-and-conquer technique; a visualization interface helps users to interactively guide the process, while an SMT-based back-end verifies each step and takes care of low-level reasoning required for parallelism.We have used the system to generate provably correct implementations of several algorithms, including some important algorithms from computational biology, and show that the performance is comparable to that of the best manually optimized code.

We introduce a framework allowing domain experts to manipulate computational terms in the interest of deriving better, more efficient implementations. It employs deductive reasoning to generate provably correct efficient implementations from a very high-level specification of an algorithm, and inductive constraint-based synthesis to improve automation. Semantic information is encoded into program terms through the use of refinement types.In this paper, we develop the technique in the context of a system called Bellmania that uses solver-aided tactics to derive parallel divide-and-conquer implementations of dynamic programming algorithms that have better locality and are significantly more efficient than traditional loop-based implementations. Bellmania includes a high-level language for specifying dynamic programming algorithms and a calculus that facilitates gradual transformation of these specifications into efficient implementations. These transformations formalize the divide-and-conquer technique; a visualization interface helps users to interactively guide the process, while an SMT-based back-end verifies each step and takes care of low-level reasoning required for parallelism.We have used the system to generate provably correct implementations of several algorithms, including some important algorithms from computational biology, and show that the performance is comparable to that of the best manually optimized code.

Abstract. The classical algorithm uses Dynamic Programming to construct an Optimal Binary Search Tree. In this paper, we research into the dynamical process of building an Optimal Binary Search Tree and present an optimized solution. Time complexity is reduced from O (n 3 ) to O (n 2 ). Meanwhile, three feasible parallel solutions are put forward to achieve greater optimization. Some experiments on cluster have been done to compare efficiency of parallel and serial algorithm and the result shows that the parallel algorithm is much better. In the case of a larger amount of testing data, the parallel solution can save half of the time consumption. However, because of the particularity of this issue, the parallel algorithm has its own limitation. IntroductionTo construct an Optimal Binary Search Tree, the classical algorithm [1] uses Dynamic Programming which will create two upper triangular matrixes dynamically to record the root node and the best search cost of the optimal sub-tree. The whole algorithm will be done after all the sub-trees have been traversed. The calculation of each cell in the matrix needs all the results that provided by other cells which are in the same line and the same column of the current cell. In this way, each position needs all the previous results which will lead to high data dependency. Meanwhile, since we need to select the root node for the current sub-tree, it is also a necessity to traverse all the key nodes between the current two key nodes. So the time complexity of classical algorithm is O (n

The FabSquare system is a personal fabrication method that lets users fabricate objects by molding photopolymers inside a 3D printed mold. The molds are printed with UV-transparent materials that allow for UV curing--the polymerization and solidification of the fluid content. The molds can be repeatedly reused to fabricate identical objects or create new objects with identical geometry, but different components. Because the necessary equipment is easily obtainable and affordable, the FabSquare approach is suitable for ordinary users in nonspecialized labs, allowing them to rapidly fabricate a range of objects. https://extras.computer.org/extra/mcg2017030034s1.mp4https://extras.computer.org/extra/mcg2017030034s2.pdf.

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