P - Systems and Context Free Languages

P systems are computing models, where certain objects can evolve in parallel into a hierarchical membrane structure. These membranes cannot preserve any order between their own objects. So, if we wish to treat their content as a sequence of characters, then any order will be correct. Thus, languages as {α|α ∈ {a, b},#a(α) = #b(α)} and {anbn|n ≥ 1} for example, are considered and treated identical. A construction which preserves the order of the characters in the words for context free languages is presented in this paper. It is made in P systems with active membranes, where all evolution rules are context free. Some preliminary decision problems concerning the words of context free languages generated with this type of P systems are considered; namely, it can be checked if there are sequences of a given length, or if two sequences are equal or not. Supported by Spanish Secretaria de Estado de Educacion, Universidades, Investigacion y Desarrollo, project SAB1999-0025