Related papers: Lemmings is PSPACE-complete
Game balancing is a longstanding challenge requiring repeated playtesting, expert intuition, and extensive manual tuning. We introduce RuleSmith, the first framework that achieves automated game balancing by leveraging the reasoning…
This paper introduces the novel task of multimodal puzzle solving, framed within the context of visual question-answering. We present a new dataset, AlgoPuzzleVQA designed to challenge and evaluate the capabilities of multimodal language…
In this paper we will be introducing a type of game which as far as this author is aware has never been studied before. These are games where there are two players, one who is trying to get one of his pieces, called a King to a predefined…
We prove computational intractability of variants of checkers: (1) deciding whether there is a move that forces the other player to win in one move is NP-complete; (2) checkers where players must always be able to jump on their turn is…
Modern board games are a rich source of interesting and new challenges for combinatorial problems. The game Nmbr9 is a solitaire style puzzle game using polyominoes. The rules of the game are simple to explain, but modelling the game…
We analyze the computational complexity of two 2-player games involving packing objects into a box. In the first game, players alternate drawing polycubes from a shared pile and placing them into an initially empty box in any available…
Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the…
Developing a consistent and reliable AI game master for text-based games is a challenging task due to the limitations of large language models (LLMs) and the complexity of the game master's role. This paper presents a novel approach to…
We analyze some of the many game mechanics available to Link in the classic Legend of Zelda series of video games. In each case, we prove that the generalized game with that mechanic is polynomial, NP-complete, NP-hard and in PSPACE, or…
We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change…
Large language models (LLMs) have demonstrated potential in reasoning tasks, but their performance on linguistics puzzles remains consistently poor. These puzzles, often derived from Linguistics Olympiad (LO) contests, provide a minimal…
The rapid advancement of large language models has accelerated their application in reasoning, with strategic reasoning drawing increasing attention. To evaluate the strategic reasoning capabilities of LLMs, game theory, with its concise…
There has been a recent explosion in the capabilities of game-playing artificial intelligence. Many classes of RL tasks, from Atari games to motor control to board games, are now solvable by fairly generic algorithms, based on deep…
Decision-making is a complex process requiring diverse abilities, making it an excellent framework for evaluating Large Language Models (LLMs). Researchers have examined LLMs' decision-making through the lens of Game Theory. However,…
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…
We develop a constrained bimatrix game framework that can be used to model many practical problems in many disciplines, including jamming in packetized wireless networks. In contrast to the widely used zero-sum framework, in bimatrix games…
Recent breakthroughs in Large Language Models (LLMs) have led to a qualitative leap in artificial intelligence' s performance on reasoning tasks, particularly demonstrating remarkable capabilities in mathematical, symbolic, and commonsense…
Wargames are simulations of conflicts in which participants' decisions influence future events. While casual wargaming can be used for entertainment or socialization, serious wargaming is used by experts to explore strategic implications of…
In recent years, Procedural Level Generation via Machine Learning (PLGML) techniques have been applied to generate game levels with machine learning. These approaches rely on human-annotated representations of game levels. Creating…
We consider the pebble game on DAGs with bounded fan-in introduced in [Paterson and Hewitt '70] and the reversible version of this game in [Bennett '89], and study the question of how hard it is to decide exactly or approximately the number…