7164901 Arden s Theorem Tafl

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Ardens theorem
  Presentation on :  Presented by:- Gaurav Gupta 20/05 IInd B.Tech I.T.   “ARDEN’S THEOREM”     CONSRTRUCTION OF REGULAR EXPRESSION FROM DFA  The regular expression is mathematical expression for a given regular language.  We know that for every regular language there exist a DFA.  We can conclude that for regular expression, regular language for that regular expression and DFA for that regular language are similar things in different representation.  So we can construct regular expression for every Deterministic Automata.   ARDEN’S THEOREM  is one means to implement it.   RDEN’S THEOREM   Let P and Q be two regular expression over alphabet Σ . If P does not contain NULL STRING ( ε ), then : R = Q + RP Has a unique solution that is : R = QP* Now lets have a look at its mathematical proof…    MATHEMATICAL PROOF It can be understood as : R = Q + R P Put the value of R in R.H.S. R = Q + (Q + RP) P = Q +QP + RP 2   When we put the value of R again and again we get the following equation: R = Q + QP + QP 2 + QP 3 …   R = Q ( 1 + P + P 2 + P 3   …) R = Q ( ε  + P + P 2 + P 3   … )   R = QP* -(By the definition of closure operation for regular expression.)
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