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The Sudoku puzzle has achieved worldwide popularity recently, and attracted great attention of the computational intelligence community. Sudoku is always considered as Satisfiability Problem or Constraint Satisfaction Problem. In this…

Artificial Intelligence · Computer Science 2009-03-11 Zhe Chen

Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…

Computer Science and Game Theory · Computer Science 2021-02-02 Pranav Ashok , Krishnendu Chatterjee , Jan Kretinsky , Maximilian Weininger , Tobias Winkler

We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an…

Data Structures and Algorithms · Computer Science 2018-04-20 Krishnendu Chatterjee , Wolfgang Dvořák , Monika Henzinger , Alexander Svozil

We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…

Discrete Mathematics · Computer Science 2007-05-23 Erik D. Demaine , Martin L. Demaine , Helena A. Verrill

Classic reachability games on graphs are zero-sum games, where the goal of one player, Eve, is to visit a vertex from a given target set, and that of other player, Adam, is to prevent this. Generalised reachability games, studied by…

Computer Science and Game Theory · Computer Science 2025-09-18 Sougata Bose , Daniel Hausmann , Soumyajit Paul , Sven Schewe , Tansholpan Zhanabekova

We study two-player multi-weighted reachability games played on a finite directed graph, where an agent, called P1, has several quantitative reachability objectives that he wants to optimize against an antagonistic environment, called P2.…

Computer Science and Game Theory · Computer Science 2025-09-08 Thomas Brihaye , Aline Goeminne

Consider an agent traversing a graph of "gadgets", each with local state that changes with each traversal by the agent. We characterize the complexity of universal traversal, where the goal is to traverse every gadget at least once, for DAG…

Computational Complexity · Computer Science 2023-11-16 Hayashi Ani , Erik Demaine , Jenny Diomidova , Dylan Hendrickson , Jayson Lynch

The main topic of this paper is motivated by a localization problem in cellular networks. Given a graph $G$ we want to localize a walking agent by checking his distance to as few vertices as possible. The model we introduce is based on a…

Building agents that can explore their environments intelligently is a challenging open problem. In this paper, we make a step towards understanding how a hierarchical design of the agent's policy can affect its exploration capabilities.…

Machine Learning · Computer Science 2018-11-19 Maruan Al-Shedivat , Lisa Lee , Ruslan Salakhutdinov , Eric Xing

We prove an n-EXPTIME lower bound for the problem of deciding the winner in a reachability game on Higher Order Pushdown Automata (HPDA) of level n. This bound matches the known upper bound for parity games on HPDA. As a consequence the…

Computer Science and Game Theory · Computer Science 2007-05-23 Thierry Cachat , Igor Walukiewicz

We prove that a variant of 2048, a popular online puzzle game, is PSPACE-Complete. Our hardness result holds for a version of the problem where the player has oracle access to the computer player's moves. Specifically, we show that for an…

Computational Complexity · Computer Science 2014-08-28 Rahul Mehta

We consider the reachability problem on transition systems corresponding to succinct one-counter machines, that is, machines where the counter is incremented or decremented by a value given in binary.

Logic in Computer Science · Computer Science 2014-07-21 Paul Hunter

As part of an effort to apply the rigorous guarantees of formal verification to multi-agent systems, the field of equilibrium analysis, also called rational verification, studies equilibria in multiplayer games to reason about system-level…

Computer Science and Game Theory · Computer Science 2026-04-28 Senthil Rajasekaran , Jean-François Raskin , Moshe Y. Vardi

Reachability games are two-player games played on a graph, where the objective of $\texttt{REACH}$ player is to reach the target set whereas the objective of $\texttt{SAFE}$ player is to stay away from the target set. Reachability games…

Artificial Intelligence · Computer Science 2026-05-12 Krishnendu Chatterjee , Ehsan Kafshdar Goharshady , Mehrdad Karrabi , Maximilian Seeliger , Đorđe Žikelić

In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally…

Systems and Control · Electrical Eng. & Systems 2021-03-23 David Fridovich-Keil , Claire J. Tomlin

In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…

Computer Science and Game Theory · Computer Science 2025-10-06 Nathalie Bertrand , Patricia Bouyer , Luc Lapointe , Corto Mascle

We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…

Computational Complexity · Computer Science 2007-05-23 Therese C. Biedl , Erik D. Demaine , Martin L. Demaine , Rudolf Fleischer , Lars Jacobsen , J. Ian Munro

We study multiplayer reachability games played on a finite directed graph equipped with target sets, one for each player. In those reachability games, it is known that there always exists a Nash equilibrium (NE) and a subgame perfect…

Computer Science and Game Theory · Computer Science 2019-07-15 Thomas Brihaye , Véronique Bruyère , Aline Goeminne , Nathan Thomasset

How can we predict the difficulty of a Sudoku puzzle? We give an overview of difficulty rating metrics and evaluate them on extensive dataset on human problem solving (more then 1700 Sudoku puzzles, hundreds of solvers). The best results…

Artificial Intelligence · Computer Science 2014-03-31 Radek Pelánek

We consider concurrent stochastic games played on graphs with reachability and safety objectives. These games can be solved by value iteration as well as strategy iteration, each of them yielding a sequence of under-approximations of the…

Computer Science and Game Theory · Computer Science 2019-09-19 Julia Eisentraut , Jan Křetínský , Alexej Rotar