New families of non real time dpda's and their decidability results

We define new families of dpda's by restricting the appearance of equivalent configurations in certain computations. These families capture the notion of a necessary usage of the stack. We discuss the equivalence and containment problems for these families and show how to maintain on-line regularity indication (i.e., how to know at each time in the computation whether the language accepted from here on is regular). As a consequence we get a linearity test for these families. We also give polynomial time algorithms to decide regularity and real time strictness for some of these families.