Candy Sharing and Chip Firing Games on Graphs

The Candy Game begins with a finite number of players sitting in a circle, each with an initial amount of candy. At each time step, each player passes half of their pile to the player on their left (with odd sized stacks receiving an extra piece of candy). The original question was whether every initial distribution of candy results in every player holding the same number of pieces after a finite number of turns. For arbitrary initial distributions, we prove asymptotically tight bounds on the final amount of candy. The diffusion chip firing game assigns integral chip amounts to each vertex of a graph. At each time step, a vertex sends a chip to each neighbor who has less chips than itself. We show that this game on the infinite path, with bounded chip labels remains bounded for all time

The New Hampshire, Vol. 105, No. 16 (Oct. 29, 2015)

An independent student produced newspaper from the University of New Hampshire

Cirquent calculus deepened

Cirquent calculus is a new proof-theoretic and semantic framework, whose main distinguishing feature is being based on circuits, as opposed to the more traditional approaches that deal with tree-like objects such as formulas or sequents. Among its advantages are greater efficiency, flexibility and expressiveness. This paper presents a detailed elaboration of a deep-inference cirquent logic, which is naturally and inherently resource conscious. It shows that classical logic, both syntactically and semantically, is just a special, conservative fragment of this more general and, in a sense, more basic logic -- the logic of resources in the form of cirquent calculus. The reader will find various arguments in favor of switching to the new framework, such as arguments showing the insufficiency of the expressive power of linear logic or other formula-based approaches to developing resource logics, exponential improvements over the traditional approaches in both representational and proof complexities offered by cirquent calculus, and more. Among the main purposes of this paper is to provide an introductory-style starting point for what, as the author wishes to hope, might have a chance to become a new line of research in proof theory -- a proof theory based on circuits instead of formulas.Comment: Significant improvements over the previous version

Spartan Daily, October 12, 1954

Volume 43, Issue 15https://scholarworks.sjsu.edu/spartandaily/12067/thumbnail.jp

A game engine designed to simplify 2D video game development

In recent years, the increasing popularity of casual games for mobile and web has promoted the development of new editors to make video games easier to create. The development of these interactive applications is on its way to becoming democratized, so that anyone who is interested, without any advanced knowledge of programming, can create them for devices such as mobile phones or consoles. Nevertheless, most game development environments rely on the traditional way of programming and need advanced technical skills, even despite today’s improvements. This paper presents a new 2D game engine that reduces the complexity of video game development processes. The game specification has been simplified, decreasing the complexity of the engine architecture and introducing a very easy-to-use editing environment for game creation. The engine presented here allows the behaviour of the game objects to be defined using a very small set of conditions and actions, without the need to use complex data structures. Some experiments have been designed in order to validate its ease of use and its capacity in the creation of a wide variety of games. To test it, users with little experience in programming have developed arcade games using the presented environment as a proof of its easiness with respect to other comparable software. Results obtained endorse the concept and the hypothesis of its easiness of use and demonstrate the engine potential