.............................................................................................................................................. ii Declaration by author ....................................................................................................................... iv Publications during candidature .............................................................................

OF LICENTIATE THESIS AALTO UNIVERSITY SCHOOL OF SCIENCE AND TECHNOLOGY P.O. BOX 11000, FI-00076 AALTO http://www.aalto.fi Author Juha-Petri Kärnä Name of the thesis Date May 25, 2010 Article thesis (summary + original articles) Monograph Faculty Department Professorship Supervisor Second examiner Abstract

Our goal is to formalize the Church-Turing Thesis for a very large class of computational models. Specifically, the notion of an “effective model of computation” over an arbitrary countable domain is axiomatized. This is accomplished by modifying Gurevich’s “Abstract State Machine” postulates for state-transition models. A proof is provided that all models satisfying these axioms, regardless of...

................................................................ iii Acknowledgements................................................... iν List of Tables ......................................................... ix List of Figures ........................................................ xii Statement of Candidate Contribution............................ xiv CHAPTER ONEIntroduction................