21,273 research outputs found

    Building Nim

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    The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new spin: building nim. With given finite numbers of tokens and stacks, this two-player game is played in two stages (thus belonging to the same family of games as e.g. nine-men's morris): first building, where players alternate to put one token on one of the, initially empty, stacks until all tokens have been used. Then, the players play nim. Of course, because the solution for the game of nim is known, the goal of the player who starts nim play is a placement of the tokens so that the Nim-sum of the stack heights at the end of building is different from 0. This game is trivial if the total number of tokens is odd as the Nim-sum could never be 0, or if both the number of tokens and the number of stacks are even, since a simple mimicking strategy results in a Nim-sum of 0 after each of the second player's moves. We present the solution for this game for some non-trivial cases and state a general conjecture

    Deciding the Winner of an Arbitrary Finite Poset Game is PSPACE-Complete

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    A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the poset loses. Polynomial time algorithms exist for certain restricted classes of poset games, such as the game of Nim. However, until recently the complexity of arbitrary finite poset games was only known to exist somewhere between NC^1 and PSPACE. We resolve this discrepancy by showing that deciding the winner of an arbitrary finite poset game is PSPACE-complete. To this end, we give an explicit reduction from Node Kayles, a PSPACE-complete game in which players vie to chose an independent set in a graph

    (MU-CTL-01-12) Towards Model Driven Game Engineering in SimSYS: Requirements for the Agile Software Development Process Game

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    Software Engineering (SE) and Systems Engineering (Sys) are knowledge intensive, specialized, rapidly changing disciplines; their educational infrastructure faces significant challenges including the need to rapidly, widely, and cost effectively introduce new or revised course material; encourage the broad participation of students; address changing student motivations and attitudes; support undergraduate, graduate and lifelong learning; and incorporate the skills needed by industry. Games have a reputation for being fun and engaging; more importantly immersive, requiring deep thinking and complex problem solving. We believe educational games are essential in the next generation of e-learning tools. An extensible, freely available, engaging, problem-based game platform that provides students with an interactive simulated experience closely resembling the activities performed in a (real) industry development project would transform the SE/Sys education infrastructure. Our goal is to extend the state-of-the-art research in SE/Sys education by investigating a game development platform (GDP) from an interdisciplinary perspective (education, game research, and software/systems engineering). A meta-model has been proposed to provide a rigourous foundation that integrates the three disciplines. The GDP is intended to support the semi-automated development of collections of scripted games and their execution, where each game embodies a specific set of learning objectives. The games are scripted using a template based approach. The templates integrate three approaches: use cases; storyboards; and state machines (timed, concurrent, hierarchical state machines). The specification templates capture the structure of the game (Game, Acts, Scenes, Screens, Challenges), storyline, characters (player, non-player, external), graphics, music/sound effects, rules, and so on. The instantiated templates are (manually) transformed into XML game scripts that can be loaded into the SimSYS Game Play Engine. As a game is played, the game play events are logged; they are analyzed to automatically assess a player’s accomplishments and automatically adapt the game play script. Currently, we are manually defining a collection of games. The games are being used to ensure the GDP is flexible and reliable (i.e., the prototype can load and correctly run a variety of game scripts), the ontology is comprehensive, and the templates assist in defining well-organized, modular game scripts. In this report, we present the initial part of an Agile Software Development Process game (Act I, Scenes 1 and 2) that embodies learning objectives related to SE fundamentals (requirements, architecture, testing, process); planning with Gantt charts; working with budgets; and selecting a team for an agile development project. A student player is rewarded in the game by getting hired, scoring points, or getting promoted to lead a project. The game has a variety of settings including a classroom, job fair, and a work environment with meeting rooms, cubicles, and a water cooler station. The main non-player characters include a teacher, boss, and an evil peer. In the future, semi-automated support for creating new game scripts will be explored using a wizard interface. The templates will be formally defined, supporting automated transformation into XML game scripts that can be loaded into the SimSYS Game Engine. We also plan to explore transforming the requirements into a notation that can be imported into a commercial tool that supports Statechart simulation

    On Aperiodic Subtraction Games with Bounded Nim Sequence

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    Subtraction games are a class of impartial combinatorial games whose positions correspond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to define, sub- traction games have proven difficult to analyze. In particular, few general results about their Sprague-Grundy values are known. In this paper, we construct an example of a subtraction game whose sequence of Sprague-Grundy values is ternary and aperiodic, and we develop a theory that might lead to a generalization of our construction.Comment: 45 page

    Impartial avoidance games for generating finite groups

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    We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The first player who cannot select an element without making the set of jointly-selected elements into a generating set for the group loses the game. We develop criteria on the maximal subgroups that determine the nim-numbers of these games and use our criteria to study our game for several families of groups, including nilpotent, sporadic, and symmetric groups.Comment: 14 pages, 4 figures. Revised in response to comments from refere
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