\contentsline {chapter}{\tocchapter {Chapter}{}{Student Plagiarism: Compliance Statement}}{ii}{chapter*.2} \contentsline {chapter}{\tocchapter {Chapter}{}{Abstract}}{iii}{chapter*.4} \contentsline {chapter}{\tocchapter {Chapter}{}{Acknowledgements}}{iv}{chapter*.6} \contentsline {chapter}{\tocchapter {Chapter}{}{List of Figures}}{vi}{chapter*.6} \contentsline {chapter}{\tocchapter {Chapter}{}{List of Tables}}{vii}{chapter*.6} \contentsline {chapter}{\tocchapter {Chapter}{1}{Introduction}}{1}{chapter.1} \contentsline {chapter}{\tocchapter {Chapter}{2}{Literature Review}}{2}{chapter.2} \contentsline {section}{\tocsection {}{2.1}{Program Semantics}}{2}{section.2.1} \contentsline {section}{\tocsection {}{2.2}{Abstract Interpretation}}{3}{section.2.2} \contentsline {subsection}{\tocsubsection {}{2.2.1}{General Framework}}{3}{subsection.2.2.1} \contentsline {subsection}{\tocsubsection {}{2.2.2}{Intervals}}{4}{subsection.2.2.2} \contentsline {subsection}{\tocsubsection {}{2.2.3}{Zones}}{4}{subsection.2.2.3} \contentsline {section}{\tocsection {}{2.3}{Min/max problem}}{4}{section.2.3} \contentsline {subsection}{\tocsubsection {}{2.3.1}{Partial-ordering Formulation}}{5}{subsection.2.3.1} \contentsline {subsubsection}{\tocsubsubsection {}{2.3.1.1}{Lattice construction}}{8}{subsubsection.2.3.1.1} \contentsline {subsection}{\tocsubsection {}{2.3.2}{Formalities}}{11}{subsection.2.3.2} \contentsline {subsection}{\tocsubsection {}{2.3.3}{Example solve}}{11}{subsection.2.3.3} \contentsline {chapter}{\tocchapter {Chapter}{3}{Evaluation}}{12}{chapter.3} \contentsline {chapter}{\tocchapter {Chapter}{4}{Experiments}}{13}{chapter.4} \contentsline {chapter}{\tocchapter {Chapter}{5}{Results}}{14}{chapter.5} \contentsline {chapter}{\tocchapter {Chapter}{6}{Conclusion}}{15}{chapter.6} \contentsline {chapter}{\tocchapter {Chapter}{}{Bibliography}}{16}{chapter*.8}