Verifying the Kleene's Theorem in a java-based visualization

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					  Verifying the Kleene’s
 Theorem in a java-based
       visualization

Click to edit Master subtitle style




                        Ramoran, Vanessa C. and Depasucat, Chat S.
                    •   Regular expression
Mathematical        •   Finite Automaton
models
                    •   Transition Graph


                                                Cohen, 1991
               Play an essential role in computer science
               They represent computer systems at
                  different level of abstraction
                Serve as simplifications at how some actual
                   machines work




                    models and diagrams can greatly improve
                   an individual’s understanding of a relatively
                          complex concept – Hurd, 2002
language             language



       language
                   Letters and alphabets

                       Set of words

           Valid instructions or programs
Kleene, 1956



         Its Proof requires a lot of attention to
         understand
         Implementing the proofs manually is very prone
         to human error and does not always give
         accurate results
    Objectives of the study




e visualizations in creating finiteaautomata or a transitionallow concate
           created machine into regular expression and graph as inpu
onvert the 3. show a visual representation at how the machines are conv
Materials and Methods
      •   Requirements Phase -
          thorough research on
          regular expressions, finite
          automata, and transition
          graphs to understand the
          concept of Kleene’s
          Theorem.
      •    
    Materials and Methods –Design
                Phase
•   Input, output and processing specifications
    were drawn up in detail
•   DFDs were created
Results and Discussion
Results and discussion

         Main Window


        FA to RE and FA
            Closure

          Concatenatio
          n and Union
rsion of finite automation to regular expression

                                       Concatenates two finite automata
   Performs union of two finite
           automata


                                  Generates the closure of a finite automato




                                                                 MAIN
Main Windows for the FA to RE
and Closure of Finite Automaton
         Applications
                    FA and RE




 Closure
 Help FA
Create Topics
   About
 Close




                .. back
  Dialog for the
number of state/s
Dialog for the
 final state/s
              Input Table




                  Show connection
                      Button
Final State
            Editable
             Table




            Convert FA
Completed
   FA
Step By Step     Direct
 Conversion    Conversion
                                New FA: State 2 has
                                  been eliminated




Old FA: State 2 has
not been eliminated   A dialog allowing user
                       to choose the next
        yet               valid state/s to
                      New FA: State 3 has
                        been eliminated
                            Shows the equivalent
Old FA: State 3 has           regular expression
not been eliminated
        yet
          Equivalent
            regular
          expression




Initial                Back

 FA
.. back
                  Clicking this
                     Input table
               enables the input
                 The (FA)* button.
                table for editing
                  Clicking this will
                      of the
                    generate the
                  connectionsthe
                   closure of
Completed FA        created FA.
                                 The equivalent RE




              The resulting FA
State Table                                 MAIN
Concatenation of Two Finite Automata
   and Union of Two Finite Automata

                         Concatenation




   Union
  Help FA
Create Topics
     About
  Close




                BACK
 Panel FA1 where
FA1 will be painted   Panel FA2 where
                      FA2 will be painted
                              States of FA1




                        Input table for
                         FA1, enabled
                     ‘Show Connection’
                     button.for use. this
                             Clicking
                       button when the
                        input table is
                     complete paints the
                      connections of the
States of FA1         FA being created.
                Final state
                                                 Back




                       Edit buttons
                        enable the
                      corresponding
                      input table for
                          editing.



                Completed FA2

                           ‘FA1FA2’ button,
                            clicking this will
                             generate the
                          concatenation of the
                                two FAs.
Completed FA1
                       ‘FA1+FA2’ button,
                         clicking this will
                       generate
                Completed FA2 the union
                         of the two FAs.
Completed FA1
The resulting FA of the
Concatenation of Two
        FAs.
                   MAIN




The resulting FA of the
  Union of Two FAs.
  Summary and Conclusion

  Verification of the Kleene’s
theorem through visualization

            •FA to RE
            •FA Closure
            •FA Concatenation
            •FA Union
Thank you