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\documentclass[11pt]{article}
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\usepackage{times}
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\usepackage{amsmath}
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\usepackage{amssymb}
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\begin{document}
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\noindent
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{\LARGE\bf Fahad's results for thesis}\bigskip
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\noindent
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Part 1 (regular expressions)
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\begin{itemize}
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\item he corrected the paper by Sulzmann and Lu by giving a new definition
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for POSIX matching---his proof is completely different than the one
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by Sulzmann and Lu and formalised in Isabelle
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\item he extended the results by Sulzmann and Lu to all regular
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expression constructors, excluding back references; to deal with
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backreferences is probably too difficult for the remaining time
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\item he formalised in Isabelle the definition of POSIX matching by Okui and
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Suzuki and showed that it is equivalent to his definition (his
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definition is declarative, whereas the one by Okui \& Suzuki is by a
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position caluculus---so both definitions are quite different
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technically, but the result is that they define the same `thing')
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\item from his correctness result for the algorithm by Sulzmann and
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Lu, he proved the correctness of various stages of optimisations: POSIX
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matching including simplification of regular expressions; bit-coded
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representation of regular expressions has not yet been done, but
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should be easy to do in the remaining time
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\end{itemize}
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\noindent
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Part 2 (TLS protocol in F-Star/internship at Microsoft Research in Cambridge)
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\begin{itemize}
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\item he added features to the F-Star language in order to verify their
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TLS parser in F-Star
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\item he created a verified byte-library for F-Star, which provides an
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API to manipulate byte sequences and indexed arrays
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\item he modified the existing TLS parser in F-Star to use his new byte
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library for the representation of strings
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\item verification of the parser is not yet done, but the hope is
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he finishes this by the end of his internship (in Sepember)
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\end{itemize}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: t
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%%% End:
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