Related papers: Lattices generated by Chip Firing Game models: cri…
Chip-firing on a directed graph is a game in which chips, a discrete commodity, are placed on the vertices of the graph and are transferred between vertices. In this paper, we study a chip-firing game on the Hasse diagram of the lattice of…
Generating high-resolution, photo-realistic images has been a long-standing goal in machine learning. Recently, Nguyen et al. (2016) showed one interesting way to synthesize novel images by performing gradient ascent in the latent space of…
Traditional compiler optimization theory distinguishes three separate classes of cache miss -- Cold, Conflict and Capacity. Tiling for cache is typically guided by capacity miss counts. Models of cache function have not been effectively…
The parallel chip-firing game is an automaton on graphs in which vertices "fire" chips to their neighbors when they have enough chips to do so. The game is always periodic, and we concern ourselves with the firing sequences of vertices. We…
Chip-firing is a combinatorial game played on a graph in which we place and disperse chips on vertices until a stable state is reached. We study a chip-firing variant played on an infinite rooted directed $k$-ary tree, where we place…
Hybrid games model cyber-physical systems (CPS), like cars, trains, and airplanes, where discrete control decisions interact with continuous physical dynamics. We use Large Language Models (LLMs) to scale formal verification and synthesis…
The Chip-firing game is a discrete dynamical system played on a graph, in which chips move along edges according to a simple local rule. Properties of the underlying graph are of course useful to the understanding of the game, but since a…
Printed Circuit Boards are the foundation for the functioning of any electronic device, and therefore are an essential component for various industries such as automobile, communication, computation, etc. However, one of the challenges…
Motivated by the notion of chip-firing on the dual graph of a planar graph, we consider `integral flow chip-firing' on an arbitrary graph $G$. The chip-firing rule is governed by ${\mathcal L}^*(G)$, the dual Laplacian of $G$ determined by…
We study chip-firing on a signed graph $G_\phi$, employing a general theory of chip-firing on invertible matrices introduced by Guzm\'an and Klivans. Here a negative edge designates an adversarial relationship, so that firing a vertex…
Humans learn by interacting with their environments and perceiving the outcomes of their actions. A landmark in artificial intelligence has been the development of deep reinforcement learning (dRL) algorithms capable of doing the same in…
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…
We study a variant of the chip-firing game called the diffusion game. In the diffusion game, we begin with some integer labelling of the vertices of a graph, interpreted as a number of chips on each vertex, and then for each subsequent step…
We discuss a class of problems which we call lattice exit models. At one level, these problems provide undergraduate level exercises in labeling the vertices of graphs (e.g., depth first search). At another level (theorems about large scale…
Many cyber-physical systems (CPS) are safety-critical, so it is important to formally verify them, e.g. in formal logics that show a model's correctness specification always holds. Constructive Differential Game Logic (CdGL) is such a logic…
Procedural Content Generation (PCG) refers to the practice, in videogames and other games, of generating content such as levels, quests, or characters algorithmically. Motivated by the need to make games replayable, as well as to reduce…
User-item interactions in recommendations can be naturally de-noted as a user-item bipartite graph. Given the success of graph neural networks (GNNs) in graph representation learning, GNN-based C methods have been proposed to advance…
The satisfiability problem for branching-time temporal logics like CTL*, CTL and CTL+ has important applications in program specification and verification. Their computational complexities are known: CTL* and CTL+ are complete for doubly…
This work investigates the factorization of finite lattices to implode selected intervals while preserving the remaining order structure. We examine how complete congruence relations and complete tolerance relations can be utilized for this…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…