powerful than DPDA s. In fact, DCFL s is a class of languages that lies properly between the class of regular languages and CFL s. The following discussion proves this fact.

Theorem : If L is a regular language, then there is some DPDA M such that .

Proof : Since L is regular, then exists a DFA D such that .

The PDA M can be constructed from D (with an additional stock) that simulates all the moves of D on any input just by ignoring its stock. That is if when Such that It is easy to see that

Again, the language can be shown to be non-regular by using pumping lemma. But, the DPDA presented in the example above accepts this language.

Hence the class of DCFL s properly includes the class of regular languages.