Descriptive Complexity of Finite Abelian Groups

Title of dissertation: MODEL THEORY AND COMPLEXITY THEORY Walid Gomaa Doctor of Philosophy, 2007 Dissertation directed by: Professor William Gasarch Department of Computer Science and Professor David Kueker Department of Mathematics Descriptive complexity theory is a branch of complexity theory that views the hardness of a problem in terms of the complexity of expressing it in some logical formalism; among the resources considered are the number of object variables, quantifier depth, type, and alternation, sentences length (finite/infinite), etc. In this field we have studied two problems: (i) expressibility in SO and (ii) the descriptive complexity of finite abelian groups. Inspired by Fagin's result that NP = SO, we have developed a partial framework to investigate expressibility inside SO so as to have a finer look into NP. The framework uses combinatorics derived from second-order Ehrenfeucht-Fra

• Type: Journal
• Year: 2010
• Where: IJAC
• Authors: Walid Gomaa
• Keywords: Complexity Theory, Descriptive Complexity, IJAC 2010, Quantifier Depth