Describing Computations by (bounded) Local Sets

We introduce the deenition of local structures as description of computations to recognize strings. Then, we identify the type of local structures corresponding to regular, context free and context sensitive languages, respectively and give a uniform characterization of those families in Chomsky's hierachy in terms of projection of frontiers of local sets of structures. In the second part, we consider another type of structures, we call bounded-grids, corresponding to local pictures with frontier equal to the bottom-right semi-perimeter. Then we study the family of string languages that are projections of frontiers of local sets of bounded-grids. This results to be included in the family of context sensitive languages, thus we refer to it as bounded context-sensitive (BCS). Moreover we show that BCS family is closed under concatenation and Kleene's star operations and under boolean union and intersection. We also construct explicitely the local bounded-grids sets for several examples of tipical context sensitive languages.