Related papers: Implicit State and Goals in QBF Encodings for Posi…
We consider 2-player stochastic games with perfectly observed actions, and study the limit, as the discount factor goes to one, of the equilibrium payoffs set. In the usual setup where current states are observed by the players, we show…
Quantum computers are on the verge of becoming a commercially available reality. They represent a paradigm shift in computing, with a steep learning gradient. The creation of games is a way to ease the transition for beginners. We present a…
Language models have shown unprecedented capabilities, sparking debate over the source of their performance. Is it merely the outcome of learning syntactic patterns and surface level statistics, or do they extract semantics and a world…
Positional encoding (PE) underpins how permutation-invariant Transformers represent sequence order, yet how positional information is processed and stored remains poorly understood. Modern PE methods such as RoPE still struggle on tasks…
Many problems in compositional synthesis and verification of multi-agent systems -- such as rational verification and assume-guarantee verification in probabilistic systems -- reduce to reasoning about two-player multi-objective stochastic…
Maker-Breaker games are played on a hypergraph $(X,\mathcal{F})$, where $\mathcal{F} \subseteq 2^X$ denotes the family of winning sets. Both players alternately claim a predefined amount of edges (called bias) from the board $X$, and Maker…
Traditional coding theory guarantees valid decoding only if a minority of symbols are adversarially manipulated. In contrast, the game of coding framework ensures reliable decoding, even in the presence of an adversarial majority. This…
Strategic interactions often take place in an environment rife with uncertainty. As a result, the equilibrium of a game is intimately related to the information available to its players. The \emph{signaling problem} abstracts the task faced…
Transformers have impressive generalization capabilities on tasks with a fixed context length. However, they fail to generalize to sequences of arbitrary length, even for seemingly simple tasks such as duplicating a string. Moreover, simply…
In many QBF encodings, sequences of Boolean variables stand for binary representations of integer variables. Examples are state labels in bounded model checking or actions in planning problems. Often not the full possible range is used,…
Positional encodings enable Transformers to incorporate sequential information, yet their theoretical understanding remains limited to two properties: distance attenuation and translation invariance. Because natural language lacks purely…
Over the last few years, much progress has been made in the theory and practice of solving quantified Boolean formulas (QBF). Novel solvers have been presented that either successfully enhance established techniques or implement novel…
We present a new dataset containing 10K human-annotated games of Go and show how these natural language annotations can be used as a tool for model interpretability. Given a board state and its associated comment, our approach uses linear…
We introduce an affine version of Tic-Tac-Toe played on the finite affine space $\mathbb{F}_q^m$. Two players alternately claim points, and the first player to occupy all points of an affine subspace of dimension $n$ wins. We call this the…
A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum…
Stackelberg equilibria have become increasingly important as a solution concept in computational game theory, largely inspired by practical problems such as security settings. In practice, however, there is typically uncertainty regarding…
Recent work in deep reinforcement learning (RL) has produced algorithms capable of mastering challenging games such as Go, chess, or shogi. In these works the RL agent directly observes the natural state of the game and controls that state…
We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…
In this work we study how explicit world-modeling objectives affect the internal representations and downstream capability of Transformers across different training stages. We use a controlled 2x2x2 Rubik's Cube and ask: (1) how does…
We introduce achievement positional games, a convention for positional games which encompasses the Maker-Maker and Maker-Breaker conventions. We consider two hypergraphs, one red and one blue, on the same vertex set. Two players, Left and…