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In recent years, reinforcement learning has seen interest because of deep Q-Learning, where the model is a convolutional neural network. Deep Q-Learning has shown promising results in games such as Atari and AlphaGo. Instead of learning the…
The mu-calculus is a powerful tool for specifying and verifying transition systems, including those with both demonic and angelic choice; its quantitative generalisation qMu extends that to probabilistic choice. We show that for a…
Large Language Models (LLMs) struggle with multi-step reasoning over structured tables. The primary reason is the lack of explicit supervision for intermediate reasoning states. Existing learned reward models or executor-based verifiers are…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
Computational models of purposeful behavior comprise both descriptive and prescriptive aspects, used respectively to ascertain and evaluate situations in the world. In reinforcement learning, prescriptive reward functions are assumed to…
Positional games are a branch of combinatorics, researching a variety of two-player games, ranging from popular recreational games such as Tic-Tac-Toe and Hex, to purely abstract games played on graphs and hypergraphs. It is closely…
We introduce a physics-inspired continuous relaxation framework that yields substantially improved solutions for NP-hard combinatorial optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), binary sparse…
We introduce and investigate symbolic proof systems for Quantified Boolean Formulas (QBF) operating on Ordered Binary Decision Diagrams (OBDDs). These systems capture QBF solvers that perform symbolic quantifier elimination, and as such…
In this paper, we perform a minimalistic quantization of the classical game of tic-tac-toe, by allowing superpositions of classical moves. In order for the quantum game to reduce properly to the classical game, we require legal quantum…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
Quantified Boolean formulas (QBFs) generalize propositional formulas by admitting quantifications over propositional variables. QBFs can be viewed as (restricted) formulas of first-order predicate logic and easy translations of QBFs into…
Infinite-state reactive synthesis has attracted significant attention in recent years, which has led to the emergence of novel symbolic techniques for solving infinite-state games. Temporal logics featuring variables over infinite domains…
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…
Conventional reward modeling relies on gradient descent over neural weights, creating opaque, data-hungry "black boxes." We propose a paradigm shift from implicit to explicit reward parameterization, recasting optimization from continuous…
We introduce the game of infinite Hex, extending the familiar finite game to natural play on the infinite hexagonal lattice. Whereas the finite game is a win for the first player, we prove in contrast that infinite Hex is a draw -- both…
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…
Decoding strategies play a pivotal role in text generation for modern language models, yet a puzzling gap divides theory and practice. Surprisingly, strategies that should intuitively be optimal, such as Maximum a Posteriori (MAP), often…
In a nonlocal game, two noncommunicating players cooperate to convince a referee that they possess a strategy that does not violate the rules of the game. Quantum strategies allow players to optimally win some games by performing joint…
We study equilibrium computation with extensive-form correlation in two-player turn-taking stochastic games. Our main results are two-fold: (1) We give an algorithm for computing a Stackelberg extensive-form correlated equilibrium (SEFCE),…
We provide two methodologies in the area of computation theory to solve optimal strategies for board games such as Xi Gua Qi and Go. From experimental results, we find relevance to graph theory, matrix representation, and mathematical…