L5

DFA  RE How to construct a RE for the following DFA? 0 q0 1 0 • By observation: (0+1)*0+0* • A systematic method? 1 q1 ARDEN’s THEOREM • Let P and Q be two Regular Expression over  . If P does not contain ,then the following equation in R, viz. R = Q+RP has a unique solution (i.e one and only one solution) given by R=QP*.  Algebraic Method using Arden’s Theorem • The following assumptions are made regarding the transition system The transition graph does not have (lambda)-moves It has only one initial states.say v1 Its vertices are v1,… vn. Vi is the R.E representing the set of string accepted by the system even though vi is a final states. 1) 2) 3) 4)  5)  ij Denotes the r.e representing the set of labels of edges from vi to vj, when there is no such edge,  ij = . Consequently we can get the following set of equations in v1 …vn.  6)  +……+ ^(lambda) V1=V1 +V2 21 11