Strategy-Stealing Is Non-Constructive

In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. This work is about the complexity behind these proofs: how hard is it to actually find a winning move in a game, when you know by strategy-stealing that one exists? We prove that this problem is PSPACE-Complete already for Minimum Poset Games and Symmetric Maker-Maker Games, which are simple classes of games that capture two of the main types of strategy-stealing arguments in the current literature

Taking Skepticism Seriously: How the Zhuang-Zi Can Inform Contemporary Epistemology

This paper explores a few of the ways that the Zhuang-Zi can inform contemporary analytic epistemology. I begin, in section 1, by briefly outlining and summarizing the case for my fictionalist interpretation of the text. In section 2, I discuss how the Zhuang-Zi can be brought into productive dialogue with the question of how we should respond to skeptical arguments. Specifically, I argue that the Zhuang-Zi can be reasonably interpreted as exemplifying an approach that is different from dominant contemporary responses to skeptical arguments in three ways: (i) it is fictionalist; (ii) it motivates a skeptical perspective rather than a claim; and (iii) it accomplishes its aims in an atypical, but nonetheless contextually appropriate, way. However, the Zhuang-Zi is relevant to contemporary debates about skeptical arguments because it can be used: (i) to respond to the same sorts of skeptical arguments that occupy contemporary commentators; (ii) to address a number of questions that arise in connection with such arguments; and (iii) to suggest important new questions for epistemologists to pursue

QuickCSG: Fast Arbitrary Boolean Combinations of N Solids

QuickCSG computes the result for general N-polyhedron boolean expressions without an intermediate tree of solids. We propose a vertex-centric view of the problem, which simplifies the identification of final geometric contributions, and facilitates its spatial decomposition. The problem is then cast in a single KD-tree exploration, geared toward the result by early pruning of any region of space not contributing to the final surface. We assume strong regularity properties on the input meshes and that they are in general position. This simplifying assumption, in combination with our vertex-centric approach, improves the speed of the approach. Complemented with a task-stealing parallelization, the algorithm achieves breakthrough performance, one to two orders of magnitude speedups with respect to state-of-the-art CPU algorithms, on boolean operations over two to dozens of polyhedra. The algorithm also outperforms GPU implementations with approximate discretizations, while producing an output without redundant facets. Despite the restrictive assumptions on the input, we show the usefulness of QuickCSG for applications with large CSG problems and strong temporal constraints, e.g. modeling for 3D printers, reconstruction from visual hulls and collision detection

Finding maximum k-cliques faster using lazy global domination

No abstract available