Particular Results for Variants of P Systems with One Catalyst in One Membrane

Abstract

Purely catalytic P systems can generate all recursively enumerable sets of natural numbers with only three catalysts in one membrane, whereas we know that one catalyst in one membrane is not enough. On the other hand, P systems also allowing (non-catalytic) non-cooperative evolution rules with only two catalysts in one membrane are already computationally complete, too. We here investigate special variants of P systems with only one catalyst in one membrane that are not computationally complete, i.e., variants of P systems with only one catalyst in one membrane that cannot generate all recursively enumerable sets of natural numbers.