A Reverse Hex Solver

We present Solrex,an automated solver for the game of Reverse Hex.Reverse Hex, also known as Rex, or Misere Hex, is the variant of the game of Hex in which the player who joins her two sides loses the game. Solrex performs a mini-max search of the state space using Scalable Parallel Depth First Proof Number Search, enhanced by the pruning of inferior moves and the early detection of certain winning strategies. Solrex is implemented on the same code base as the Hex program Solver, and can solve arbitrary positions on board sizes up to 6x6, with the hardest position taking less than four hours on four threads.Comment: Presented at Computers and Games 2016 Leiden, International Conference on Computers and Games. Springer International Publishing, 201

Pgx: Hardware-accelerated Parallel Game Simulators for Reinforcement Learning

We propose Pgx, a suite of board game reinforcement learning (RL) environments written in JAX and optimized for GPU/TPU accelerators. By leveraging auto-vectorization and Just-In-Time (JIT) compilation of JAX, Pgx can efficiently scale to thousands of parallel executions over accelerators. In our experiments on a DGX-A100 workstation, we discovered that Pgx can simulate RL environments 10-100x faster than existing Python RL libraries. Pgx includes RL environments commonly used as benchmarks in RL research, such as backgammon, chess, shogi, and Go. Additionally, Pgx offers miniature game sets and baseline models to facilitate rapid research cycles. We demonstrate the efficient training of the Gumbel AlphaZero algorithm with Pgx environments. Overall, Pgx provides high-performance environment simulators for researchers to accelerate their RL experiments. Pgx is available at https://github.com/sotetsuk/pgx.Comment: 9 page

Complexity, Heuristic, and Search Analysis for the Games of Crossings and Epaminondas

Games provide fertile research domains for algorithmic research. Often, game research helps solve real-world problems through the testing and refinement of search algorithms in game domains. Other times, game research finds limits for certain algorithms. For example, the game of Go proved intractable for the Min-Max with Alpha-Beta pruning algorithm leading to the popularity of Monte-Carlo based search algorithms. Although effective in Go, and game domains once ruled by Alpha-Beta such as Lines of Action, Monte-Carlo methods appear to have limits too as they fall short in tactical domains such as Hex and Chess. In a continuation of this type of research, two new games, Crossings and Epaminondas, are presented, analyzed and used to test two Monte-Carlo based algorithms: Upper Confidence Bounds applied to Trees (UCT) and Heuristic Guided UCT (HUCT). Results indicate that heuristic knowledge can positively affect UCT\u27s performance in the lower complexity domain of Crossings. However, both agents perform worse in the higher complexity domain of Epaminondas. This identifies Epaminondas as another domain that poses difficulties for Monte Carlo agents

A Local-Pattern Related Look-Up Table

This paper describes a Relevance-Zone pattern table (RZT) that can be used to replace a traditional transposition table. An RZT stores exact game values for patterns that are discovered during a Relevance-Zone-Based Search (RZS), which is the current state-of-the-art in solving L&D problems in Go. Positions that share the same pattern can reuse the same exact game value in the RZT. The pattern matching scheme for RZTs is implemented using a radix tree, taking into consideration patterns with different shapes. To improve the efficiency of table lookups, we designed a heuristic that prevents redundant lookups. The heuristic can safely skip previously queried patterns for a given position, reducing the overhead to 10% of the original cost. We also analyze the time complexity of the RZT both theoretically and empirically. Experiments show the overhead of traversing the radix tree in practice during lookup remain flat logarithmically in relation to the number of entries stored in the table. Experiments also show that the use of an RZT instead of a traditional transposition table significantly reduces the number of searched nodes on two data sets of 7x7 and 19x19 L&D Go problems.Comment: Submitted to IEEE Transactions on Games (under review

Optimizing tone production on a 300 spot per inch laser printer

Digital halftones as output on plain paper are the focus of this study. A new terminology is suggested to allow proper description of digital halftones. The most important of these terms is the use of addressability to replace the often misused term resolution. Also important is the use of the term spot rather than dot to describe addressability. A means of properly describing digital halftones is suggested to avoid confusion with analog (ie., conventional photographic) halftones. Halftone patterns were created to test the efficiency of different designs at 300 spot per inch addressability on a laser printer. The page description language PostScript was used to create the halftone patterns which were modeled on three basic designs. It has been established that two halftone dot patterns constructed on the same matrix and containing the same number of spots will produce different densities if the configuration of the spots within the matrix is different This has been tested by comparing the results of the tone production curves of the condensed and open halftone dot designs. These patterns were output on a laser printer and measured for density. Tone production curves were drawn and compared. Even though each matrix contains the same number of spots, it has been shown that different densities result. This is solely a consequence of the dot design. Microscopic studies were conducted to illustrate the nature of the filling-in in the non-image area. Microscopic measurements were also made to ascertain the size of an individual spot at various screen rulings. It was found that the spot, which was very irregular to begin with, actually began to break up as the linescreen approached 150 lines per inch. Paper tests were run to gauge the maximum density and the tone production capabilities of various papers. Although the results were inconclusive, they point out another flaw of digital halftones which are output on plain paper. The number of grays predictable, given a matrix size, is greater than what is achievable in practice. These results mean the following for designers of digital halftones. First, purely due to the nature of digital halftones, the highlight and shadow areas will be most difficult to control. Secondly, use of a screen angle can limit the filling-in in the tone production curve. Thirdly, the variability of the spot size on paper, and its irregularities must be closely observed to assure that these dot forms will be reproducible in the lithographic process if this is desired. And finally, careful planning in the design of a halftone dot may allow an improved tone production curve

Master of Science

thesisHigh energy materials are commonly used as solid rocket motors propellants. The properties of HE materials can be determined experimentally; however, the hazards associated with experiments on these materials, as well as the costs, make this approach unattractive. The simulations of these materials require techniques that can bridge submicron scales and engineering scales. Micromechanics provides such techniques. The objective of this research is to investigate the effects of stress bridging on predicting the effective properties of high energy materials group. The research focused on polymer bonded explosives (PBXs), since detailed numerical simulations of PBXs are computationally expensive. The generalized method of cells was explored for this research and its predictions of elastic moduli with and without stress bridging. The results show that stress bridging affects the estimated properties considerably. The generalized method of cells without stress bridging is shown to underestimate the elastic moduli of the polymer bonded explosives. Micromechanics analysis requires that the fundamental material properties of the constituents are known initially. The composite material properties can be determined experimentally by testing actual composite specimens. However, in recent years, more and more attention has been given to the development of the analytical and numerical models for predicting composite material properties from the properties of the constituent materials and their relationship to each other. The other part of this research is to identify the Representative Volume Element (RVE) and the boundary conditions for calculation of transverse shear modulus (G23) and then compare the results to the other classical micromechanics solutions. The results show that the proposed approach for identifying the Representative Volume Element (RVE) and the boundary conditions predict as accurately as the other classical micromechanics solutions