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Full-Text Articles in Theory and Algorithms
A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler
A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler
Senior Independent Study Theses
Santorini is a two player combinatorial board game. Santorini bears resemblance to the graph theory game of Geography, a game of moving and deleting vertices on a graph. We explore Santorini with game theory, complexity theory, and artificial intelligence. We present David Lichtenstein’s proof that Geography is PSPACE-hard and adapt the proof for generalized forms of Santorini. Last, we discuss the development of an AI built for a software implementation of Santorini and present a number of improvements to that AI.
Landing Throttleable Hybrid Rockets With Hierarchical Reinforcement Learning In A Simulated Environment, Francesco Alessandro Stefano Mikulis-Borsoi
Landing Throttleable Hybrid Rockets With Hierarchical Reinforcement Learning In A Simulated Environment, Francesco Alessandro Stefano Mikulis-Borsoi
Honors Theses and Capstones
In this paper, I develop a hierarchical Markov Decision Process (MDP) structure for completing the task of vertical rocket landing. I start by covering the background of this problem, and formally defining its constraints. In order to reduce mistakes while formulating different MDPs, I define and develop the criteria for a standardized MDP definition format. I then decompose the problem into several sub-problems of vertical landing, namely velocity control and vertical stability control. By exploiting MDP coupling and symmetrical properties, I am able to significantly reduce the size of the state space compared to a unified MDP formulation. This paper …