Here is the formal definition of the language which a string belongs to if it has been successfully parsed using an embedded push down automata :

C\left(M\right)=\left{q,{\gamma}_m ... {\gamma}_1,x_1,x_2\right} \epsilon Q \mathbb{X} (\Gamma^+)* \mathbb{X} \Sigma^* \mathbb{X} \Sigma^*

More equations and notes from my research on mildly context sensitive grammars and their describing automaton will make their way to the blog soon.