Related papers: Ludii and XCSP: Playing and Solving Logic Puzzles
Various forms of sorting problems have been studied over the years. Recently, two kinds of sorting puzzle apps are popularized. In these puzzles, we are given a set of bins filled with colored units, balls or water, and some empty bins.…
Constraint satisfaction problems (CSPs) are ubiquitous in theoretical computer science. We study the problem of StrongCSPs, i.e. instances where a large induced sub-instance has a satisfying assignment. More formally, given a CSP instance…
Ludii is a general game system being developed as part of the ERC-funded Digital Ludeme Project (DLP). While its primary aim is to model, play, and analyse the full range of traditional strategy games, Ludii also has the potential to…
This paper describes three different optimised implementations of playouts, as commonly used by game-playing algorithms such as Monte-Carlo Tree Search. Each of the optimised implementations is applicable only to specific sets of games,…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
Constraint satisfaction problems (CSPs) are a natural class of decision problems where one must decide whether there is an assignment to variables that satisfies a given formula. Schaefer's dichotomy theorem, and its extension to all…
The Reward-Penalty-Selection Problem (RPSP) can be seen as a combination of the Set Cover Problem (SCP) and the Hitting Set Problem (HSP). Given a set of elements, a set of reward sets, and a set of penalty sets, one tries to find a subset…
Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between…
This paper investigates the performance of different general-game-playing heuristics for games in the Ludii general game system. Based on these results, we train several regression learning models to predict the performance of these…
We study the computational complexity of the Buttons \& Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for $C = 2$ colors but polytime solvable for $C = 1$.…
In this Part II, we apply the general theory developed in Part I to a detailed analysis of the Constraint Satisfaction Problem (CSP). We show how specific types of resolution rules can be defined. In particular, we introduce the general…
The author has long enjoyed using the CSP refinement checker FDR to solve puzzles, as witnessed by examples in \cite{tpc,ucs}. Recent experiments have shown that a number of games of patience (card games for one) are now well within bounds.…
We analyze Solo Chess puzzles, where the input is an $n \times n$ board containing some standard Chess pieces of the same color, and the goal is to make a sequence of capture moves to reduce down to a single piece. Prior work analyzes this…
Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability…
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…
We propose discrete diffusion guidance for constraint satisfaction problems (CSPs) and demonstrate its ability to solve Sudoku puzzles without supervision.
Solving puzzles in natural language poses a long-standing challenge in AI. While large language models (LLMs) have recently shown impressive capabilities in a variety of tasks, they continue to struggle with complex puzzles that demand…
Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by…
Challenges for physical solitaire puzzle games are typically designed in advance by humans and limited in number. Alternatively, some games incorporate rules for stochastic setup, where the human solver randomly sets up the game board…