Related papers: Implicit State and Goals in QBF Encodings for Posi…
Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the…
Open parity games are proposed as a compositional extension of parity games with algebraic operations, forming string diagrams of parity games. A potential application of string diagrams of parity games is to describe a large parity game…
Current quantum simulators are primarily qubit-based, making them naturally suitable for simulating 2-level quantum systems. However, many systems in nature are inherently $d$-level, including higher spins, bosons, vibrational modes, and…
Two-player games on graphs provide the mathematical foundation for the study of reactive systems. In the quantitative framework, an objective assigns a value to every play, and the goal of player 1 is to minimize the value of the objective.…
Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…
We construct surface codes corresponding to genus greater than one in the context of quantum error correction. The architecture is inspired by the topology of invariant integral surfaces of certain non-integrable classical billiards.…
The application of Generative Pre-trained Transformer (GPT-2) to learn text-archived game notation provides a model environment for exploring sparse reward gameplay. The transformer architecture proves amenable to training on solved text…
We study finite-memory (FM) determinacy in games on finite graphs, a central question for applications in controller synthesis, as FM strategies correspond to implementable controllers. We establish general conditions under which FM…
In the natural generalization of tic-tac-toe to an $n \times n \times n$ board where $n \in \mathbb{N}$, it is known that the first player has a winning strategy if $n \leq 4$ and that either player can force a draw if $n \geq 8$. The…
The existential k-pebble game characterizes the expressive power of the existential-positive k-variable fragment of first-order logic on finite structures. The winner of the existential k-pebble game on two given finite structures can be…
We consider two-player random extensive form games where the payoffs at the leaves are independently drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for…
The object of this study are countably infinite games with perfect information that allow players to choose among arbitrarily many moves in a turn; in particular, we focus on the generalisations of the finite board games of Hex and…
We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and Haah 3D code. The…
Text-based games (TBGs) have emerged as an important collection of NLP tasks, requiring reinforcement learning (RL) agents to combine natural language understanding with reasoning. A key challenge for agents attempting to solve such tasks…
Large language models (LLMs) have been observed to suddenly exhibit advanced reasoning abilities during reinforcement learning (RL), resembling an ``aha moment'' triggered by simple outcome-based rewards. While RL has proven effective in…
Transformer-based large language models (LLMs) have demonstrated strong reasoning abilities across diverse fields, from solving programming challenges to competing in strategy-intensive games such as chess. Prior work has shown that LLMs…
This work introduces efficient symbolic algorithms for quantitative reactive synthesis. We consider resource-constrained robotic manipulators that need to interact with a human to achieve a complex task expressed in linear temporal logic.…
State estimation uncertainty is prevalent in real-world applications, hindering the application of safety-critical control. Existing methods address this by strengthening a Control Barrier Function (CBF) condition either to handle actuation…
We consider linear-quadratic Gaussian (LQG) games in which players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution conditional on…
Dependency quantified Boolean formulas (DQBF) is a logic admitting existential quantification over Boolean functions, which allows us to elegantly state synthesis problems in verification such as the search for invariants, programs, or…