Related papers: The Computational Complexity of Angry Birds
The "War of Attrition" is a classical game theoretic model that was first introduced to mathematically describe certain non-violent animal behavior. The original setup considers two participating players in a one-shot game competing for a…
We study two-player zero-sum concurrent stochastic games with finite state and action space played for an infinite number of steps. In every step, the two players simultaneously and independently choose an action. Given the current state…
In the popular computer game of Tetris, the player is given a sequence of tetromino pieces and must pack them into a rectangular gameboard initially occupied by a given configuration of filled squares; any completely filled row of the…
Game AI competitions are important to foster research and development on Game AI and AI in general. These competitions supply different challenging problems that can be translated into other contexts, virtual or real. They provide…
The rapid pace of recent research in AI has been driven in part by the presence of fast and challenging simulation environments. These environments often take the form of games; with tasks ranging from simple board games, to competitive…
We settle two long-standing complexity-theoretical questions-open since 1981 and 1993-in combinatorial game theory (CGT). We prove that the Grundy value (a.k.a. nim-value, or nimber) of Undirected Geography is PSPACE-complete to compute.…
This paper contributes a new way to evaluate AI. Much as one might evaluate a machine in terms of its performance at chess, this approach involves evaluating a machine in terms of its performance at a game called "MAD Chairs". At the time…
We study games with reachability objectives under energy constraints. We first prove that under strict energy constraints (either only lower-bound constraint or interval constraint), those games are LOGSPACE-equivalent to energy games with…
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…
A growing number of machine learning architectures, such as Generative Adversarial Networks, rely on the design of games which implement a desired functionality via a Nash equilibrium. In practice these games have an implicit complexity…
The study of system complexity primarily has two objectives: to explore underlying patterns and to develop theoretical explanations. Pattern exploration seeks to clarify the mechanisms behind the emergence of system complexity, while…
In order to build AI we have to create a program which copes well in an arbitrary world. In this paper we will restrict our attention on one concrete world, which represents the game Tick-Tack-Toe. This world is a very simple one but it is…
Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…
Priced timed games are optimal-cost reachability games played between two players---the controller and the environment---by moving a token along the edges of infinite graphs of configurations of priced timed automata. The goal of the…
With breakthrough of the AlphaGo, human-computer gaming AI has ushered in a big explosion, attracting more and more researchers all around the world. As a recognized standard for testing artificial intelligence, various human-computer…
Game theory provides an effective way to model strategic interactions among rational agents. In the context of formal verification, these ideas can be used to produce guarantees on the correctness of multi-agent systems, with a diverse…
Background: Stress has become a widespread phenomenon, and serious games are increasingly recognized as engaging tools for stress relief. However, despite the rapid advancement of Generative Artificial Intelligence (Gen-AI), its integration…
We study routing games where every agent sequentially decides her next edge when she obtains the green light at each vertex. Because every edge only has capacity to let out one agent per round, an edge acts as a FIFO waiting queue that…
We study the complexity of the popular one player combinatorial game known as Flood-It. In this game the player is given an n by n board of tiles where each tile is allocated one of c colours. The goal is to make the colours of all tiles…
In this article, we study the decision-making process of chess players by using a chess engine to evaluate the moves across different pools of games. We quantified the decisiveness of each move during the games using a metric derived from…