Using Tree Automata to Investigate Intuitionistic Propositional Logic

Intuitionistic logic is an important variant of classical logic, but it is not as well-understood, even in the propositional case. In this thesis, we describe a faithful representation of intuitionistic propositional formulas as tree automata. This representation permits a number of consequences, including a characterization theorem for free Heyting algebras, which are the intutionistic analogue of free Boolean algebras, and a new algorithm for solving equations over intuitionistic propositional logic.sachusetts and started graduate school at Cornell University. He received his PhD from Cornell in 2008. iii I dedicate this thesis to my parents, iv ACKNOWLEDGEMENTS I'd like to thank first and foremost Richard Shore and Anil Nerode, with whom I had many useful conversations and who gave me much support during my time at Cornell. I'd also like to thank Andrew Myers for teaching an excellent class on programming languages from which I first learned about intuitionistic logic. Other people with whom I had stimulating conversations about intuitionistic logic and other topics surrounding this thesis that I'd like to thank include: Gu