Related papers: Lemmings is PSPACE-complete
We prove PSPACE-completeness of Push-1: given a rectangular grid of 1 x 1 cells, each possibly occupied by a movable block, can a robot move from one specified location to another, given the ability to push up to one block at a time? In…
This paper examines the integration of computational complexity into game theoretic models. The example focused on is the Prisoner's Dilemma, repeated for a finite length of time. We show that a minimal bound on the players' computational…
Large Language Models' (LLMs) programming capabilities enable their participation in open-source games: a game-theoretic setting in which players submit computer programs in lieu of actions. These programs offer numerous advantages,…
The role of a Dungeon Master, or DM, in the game Dungeons & Dragons is to perform multiple tasks simultaneously. The DM must digest information about the game setting and monsters, synthesize scenes to present to other players, and respond…
Resolving Python dependency issues remains a tedious and error-prone process, forcing developers to manually trial compatible module versions and interpreter configurations. Existing automated solutions, such as knowledge-graph-based and…
The reversible pebble game is a combinatorial game played on rooted DAGs. This game was introduced by Bennett (1989) motivated by applications in designing space efficient reversible algorithms. Recently, Chan (2013) showed that the…
This paper examines the reasoning capabilities of Large Language Models (LLMs) from a novel perspective, focusing on their ability to operate within formally specified, rule-governed environments. We evaluate four LLMs (Gemini 2.5 Pro and…
It has been established in recent work that Large Language Models (LLMs) can be prompted to "self-play" conversational games that probe certain capabilities (general instruction following, strategic goal orientation, language understanding…
We study the Maker-Maker version of the domination game introduced in 2018 by Duch\^ene et al. Given a graph, two players alternately claim vertices. The first player to claim a dominating set of the graph wins. As the Maker-Breaker…
We consider combinatorial avoidance and achievement games based on graph Ramsey theory: The players take turns in coloring still uncolored edges of a graph G, each player being assigned a distinct color, choosing one edge per move. In…
We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit…
Many games are reliant on creating new and engaging content constantly to maintain the interest of their player-base. One such example are puzzle games, in such it is common to have a recurrent need to create new puzzles. Creating new…
Permutation Mastermind is a version of the classical mastermind game in which the number of positions $n$ is equal to the number of colors $k$, and repetition of colors is not allowed, neither in the codeword nor in the queries. In this…
In imperfect-information games, the optimal strategy in a subgame may depend on the strategy in other, unreached subgames. Thus a subgame cannot be solved in isolation and must instead consider the strategy for the entire game as a whole,…
Two new techniques are introduced into the theory of the domination game. The cutting lemma bounds the game domination number of a partially dominated graph with the game domination number of suitably modified partially dominated graph. The…
In this paper, we introduce a combination of novel and exciting tasks: the solution and generation of linguistic puzzles. We focus on puzzles used in Linguistic Olympiads for high school students. We first extend the existing benchmark for…
We introduce a problem set-up we call the Iterated Matching Pennies (IMP) game and show that it is a powerful framework for the study of three problems: adversarial learnability, conventional (i.e., non-adversarial) learnability and…
Recent research has demonstrated that large language models (LLMs) can support experts across various domains, including game design. In this study, we examine the utility of medium-sized LLMs, models that operate on consumer-grade hardware…
We define a new impartial combinatorial game, Flag Coloring, based on flood filling. We then generalize to a graph game, and find values for many positions on two colors. We demonstrate that the generalized game is PSPACE-complete for two…
The act and experience of programming is, at its heart, a fundamentally human activity that results in the production of artifacts. When considering programming, therefore, it would be a glaring omission to not involve people who specialize…