Molecular computing with generalized homogeneous P-systems

Abstract

Recently P-systems were introduced by Gheorghe Păun as a new model for computations based on membrane structures. The basic variants of P-systems shown to have universal computational power only took account of the multiplicities of atomic objects, some other variants considered rewriting rules on strings. Using the membranes as a kind of filter for specific objects when transferring them into an inner compartment or out into the surrounding compartment turned out to be a very powerful mechanism in combination with suitable rules to be applied within the membranes in the model of generalized P-systems, GP-systems for short. GP-systems were shown to allow for the simulation of graph controlled grammars of arbitrary type based on productions working on single objects; moreover, various variants of GP-systems using splicing or cutting and recombination of strings were shown to have universal computational power, too. In this paper, we consider GP-systems with homogeneous membrane structures, GhP-systems for short, using splicing or cutting and recombination of string objects with specific markers at the ends of the strings that can be interpreted as electrical charges. The sum of these electrical charges determines the permeability of the membranes to the string objects, and we allow only objects with the absolute value of the difference of electrical charges being equal to 1 to pass a membrane in both directions. We show that such GhP-systems have universal computational power; for GhP-systems using splicing and a bounded number of markers the obtained results are optimal with respect to the underlying membrane structure. Moreover, a very restricted variant of such GhP-systems characterizes the (strictly) minimal linear languages.