City University of New York (CUNY) CUNY Academic Works All Dissertations, Theses, and Capstone Projects Dissertations, Theses, and Capstone Projects 10-2014 The Computational Complexity of Some Games and Puzzles With Theoretical Applications Vasiliki Despoina Mitsou Graduate Center, City University of New York How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/gc_etds/326 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact:
[email protected] THE COMPUTATIONAL COMPLEXITY OF SOME GAMES AND PUZZLES WITH THEORETICAL APPLICATIONS by Vasiliki - Despoina Mitsou A dissertation submitted to the Graduate Faculty in Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The City University of New York 2014 This manuscript has been read and accepted for the Graduate Faculty in Computer Science in satisfaction of the dissertation requirements for the degree of Doctor of Philosophy. Amotz Bar-Noy Date Chair of Examining Committee Robert Haralick Date Executive Officer Matthew Johnson Noson Yanofsky Christina Zamfirescu Kazuhisa Makino Efstathios Zachos Supervisory Committee THE CITY UNIVERSITY OF NEW YORK ii abstract The Computational Complexity of Some Games and Puzzles with Theoretical Applications by Vasiliki Despoina Mitsou Adviser: Amotz Bar-Noy 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.