ChengsongTanPhdThesis/Chapters/Bitcoded1.tex
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     7 %Then we illustrate how the algorithm without bitcodes falls short for such aggressive 
     7 %Then we illustrate how the algorithm without bitcodes falls short for such aggressive 
     8 %simplifications and therefore introduce our version of the bitcoded algorithm and 
     8 %simplifications and therefore introduce our version of the bitcoded algorithm and 
     9 %its correctness proof in 
     9 %its correctness proof in 
    10 %Chapter 3\ref{Chapter3}. 
    10 %Chapter 3\ref{Chapter3}. 
    11 In this chapter, we are going to describe the bit-coded algorithm
    11 In this chapter, we are going to describe the bit-coded algorithm
    12 introduced by Sulzmann and Lu \parencite{Sulzmann2014} to address the growth problem of 
    12 introduced by Sulzmann and Lu \parencite{Sulzmann2014} and their correctness proof.
    13 derivatives of
    13 %to address the growth problem of 
    14 regular expressions. 
    14 %derivatives of
       
    15 %regular expressions. 
    15 We have implemented their algorithm in Scala and Isabelle, 
    16 We have implemented their algorithm in Scala and Isabelle, 
    16 and found problems 
    17 and found problems 
    17 in their algorithm, such as de-duplication not working properly and redundant
    18 in their algorithm, such as de-duplication not working properly and redundant
    18 fixpoint construction. 
    19 fixpoint construction. 
    19 \section{The Motivation Behind Using Bitcodes}
    20 \section{The Motivation Behind Using Bitcodes}