Extended Transition Function

A function ${\delta }^{\ast }:Q\times {\Sigma }^{\ast }\to Q$ denoting the transition states. Can be recursively defined by Transition Function.

$${\delta }^{\ast }(q,x)=\{\begin{array}{ll}q& \text{ if x = eps}\\ \delta ({\delta }_3^{\ast }(q,y),a)& \text{ if x = ya where }y\in {\Sigma }^{\ast },a\in \Sigma \end{array}$$