ii DEDICATION To Kimberly

A key issue in software evolution analysis is being able to compute evolutionary change accurately and with rich semantics. This dissertation describes a mathematical framework for enabling accurate computation of semantic evolutionary change. It is based on graphs for representing software semantics, graph transformations for modeling evolution, and effects of graph transformations for capturing evolutionary change. We formulate the notions of evolution sets and the evolution distance to measure evolutionary change. Then, we define an appropriate notion of optimal graph alignment to compute evolutionary change accurately. Establishing a rigorous foundation for computing evolutionary change is important for developing powerful automated tools for software evolution analysis. Cost estimation, software merging, reliability analysis, clone detection, incremental testing, validation and other software applications can benefit from precise computation of evolutionary change. A rigorous foundation also allows leveraging the extensive research on graph alignments to advance software engineering. We have created a framework for experimental evaluation of graph alignment algorithms. The framework includes a graph testbed, an accuracy metric, and a graph alignment visualization (GAV) mechanism. The framework is targeted at applications where a precise computation of evolutionary change from one system to the next is needed to reveal valuable knowledge about the system and its evolution. The accuracy metric is based on a new measure for graph difference and a new notion of optimality of graph alignment. The metric is designed to measure the degree to which an alignment is inaccurate, that is the degree to which it reports spurious differences. Such a metric is meaningful for estimating the efficiency of and resources necessary for many software evolution analyses.