It is known that the polarizationless P systems of the kind involved in the definition of the P conjecture are able to solve problems in the complexity class
by leveraging their uniformity condition. Here, we show that they are indeed able to simulate a deterministic Turing machine working in polynomial time with a weaker uniformity condition and using only one level of membrane nesting. This allows us to embed this construction into more complex membrane structures, possibly showing that constructions similar to the one performed for P systems with charges can be carried on.
