So how are we going to do it? Well before we start with coding, it is necessary to explain the mathematical background needed to fully understand the method used here in this article. I would strongly recommend to read and understand the math behind, because once we overcome the math part, the rest will be very simple. Note however that I will not have any mathematical proofs. If you are interested in proofs, please check out the references, which could be found in References section of this article. Additionally, note that the regular expression parser, which we will create here will support these three operations:

RegularExpression\Map.cs
.................\NfaDiagram.txt
.................\NfaExpression.cs
.................\NfaToDfaHelper.cs
.................\Properties
.................\..........\AssemblyInfo.cs
.................\..........\Resources.Designer.cs
.................\..........\Resources.resx
.................\..........\Settings.Designer.cs
.................\..........\Settings.settings
.................\RegEx.cs
.................\RegExValidator.cs
.................\RegularExpression.csproj
.................\Set.cs
.................\State.cs
RegularExpression
RegExImpl.sln
Driver\Driver.csproj
......\frmNfa.cs
......\frmNfa.Designer.cs
......\frmNfa.resx
......\MatchInfoDS.cs
......\MatchInfoDS.Designer.cs
......\MatchInfoDS.xsc
......\MatchInfoDS.xsd
......\MatchInfoDS.xss
......\Program.cs
......\Properties
......\..........\AssemblyInfo.cs
......\..........\Resources.Designer.cs
......\..........\Resources.resx
......\..........\Settings.Designer.cs
......\..........\Settings.settings
Driver

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