The Computational Complexity of Some Games and Puzzles With Theoretical Applications

The subject of this thesis is the algorithmic properties of one- and two-player games people enjoy playing, such as Sudoku or Chess. Questions asked about puzzles and games in this context are of the following type: can we design efficient computer programs that play optimally given any opponent (for a two-player game), or solve any instance of the puzzle in question? We examine four games and puzzles and show algorithmic as well as intractability results. First, we study the wolf-goat-cabbage puzzle, where a man wants to transport a wolf, a goat, and a cabbage across a river by using a boat that can carry only one item at a time, making sure that no incompatible items are left alone together. We study generalizations of this puzzle, showing a close connection with the Vertex Cover problem that implies NP-hardness as well as inapproximability results. Second, we study the SET game, a card game where the objective is to form sets of cards that match in a certain sense using cards from a special deck. We study single- and multi-round variations of this game and establish interesting con- nections with other classical computational problems, such as Perfect Multi- Dimensional Matching, Set Packing, Independent Edge Dominating Set, and Arc Kayles. We prove algorithmic and hardness results in the classical and the parameterized sense. Third, we study the UNO game, a game of colored numbered cards where players take turns discarding cards that match either in color or in number. We extend results by Demaine et. al. (2010 and 2014) that connected one- and two-player generaliza- tions of the game to Edge Hamiltonian Path and Generalized Geography, proving that a solitaire version parameterized by the number of colors is fixed param- eter tractable and that a k-player generalization for k greater or equal to 3 is PSPACE-hard. Finally, we study the Scrabble game, a word game where players are trying to form words in a crossword fashion by placing letter tiles on a grid board. We prove that a generalized version of Scrabble is PSPACE-hard, answering a question posed by Demaine and Hearn in 2008

Alat Permainan Edukatif Scrabble Untuk Meningkatkan Kemampuan Membaca Permulaan Anak Kelompok B

Penelitian ini bertujuan: (1) untuk mengetahui alat permainan edukatif scrabble yang layak terhadap kemampuan membaca permulaan anak kelompok B, dan (2) untuk mengetahui keefektifan alat permainan edukatif scrabble terhadap kemampuan membaca permulaan anak kelompok B. Penelitian ini menggunakan model Borg Gall. Desain pengembangan tersebut disimpulkan menjadi tiga langkah umum, yang meliputi: (1) studi pendahuluan, (2) proses pengembangan, dan (3) uji coba produk. Subjek penelitian adalah anak kelompok B TK ABA Teros. Pengumpulan data menggunakan pedoman wawancara, lembar validasi, angket penilaian guru, dan lembar observasi. Teknik analisis data menggunakan paired sample t-test dengan taraf signifikansi 0,05. Hasil penelitian menunjukkan bahwa produk yang dikembangkan efektif. Terdapat perbedaan hasil akhir antara hasil sebelum diberi perlakuan dengan sesudah diberi perlakuan menggunakan alat permainan edukatif scrabbel dengan p 0,05 kemudian terjadi peningkatan yang signifikan dengan p = 0,00

Intelligence artificielle et optimisation avec parallélisme

This document is devoted to artificial intelligence and optimization. This part will bedevoted to having fun with high level ideas and to introduce the subject. Thereafter,Part II will be devoted to Monte-Carlo Tree Search, a recent great tool for sequentialdecision making; we will only briefly discuss other tools for sequential decision making;the complexity of sequential decision making will be reviewed. Then, part IIIwill discuss optimization, with a particular focus on robust optimization and especiallyevolutionary optimization. Part IV will present some machine learning tools, useful ineveryday life, such as supervised learning and active learning. A conclusion (part V)will come back to fun and to high level ideas.On parlera ici de Monte-Carlo Tree Search, d'UCT, d'algorithmes évolutionnaires et d'autres trucs et astuces d'IA;l'accent sera mis sur la parallélisation