Infinite Versions of Some Problems from Finite Complexity Theory

Infinite Versions of Some Problems From Finite Complexity Theory

Recently, several authors have explored the connections between NP-complete problems for finite objects and the complexity of their analogs for infinite objects. In this paper, we will categorize infinite versions of several problems arising from finite complexity theory in terms of their recursion theoretic complexity and proof theoretic strength. These infinite analogs can behave in a variety...

On Some Complexity Problems in Finite Algebras

Dedicated to my wife, Regina, with my everlasting love. ii ACKNOWLEDGMENTS I would like to express my gratitude to a number of people without whose support this thesis would not have been possible. I could not possibly mention all of them. First and foremost I would like to thank my advisor, Professor Ralph McKenzie. I would like to thank him for all the seminars I had the privilege to attend, ...

Complexity of Some Infinite Games Played on Finite Graphs

Some Connections between Finite and Infinite Model Theory

Most of the work in model theory has, so far, considered infinite structures and the methods and results that have been worked out in this context can usually not be transferred to the study of finite structures in any obvious way; in addition, some basic results from infinite model theory fail within the context of finite models. The theory about finite structures has largely developed in conn...

Some Connections between Finite and Infinite Model Theory