# A Turing machine simulation by P systems without charges

## TL;DR

This paper demonstrates that a simplified class of P systems without charges can simulate deterministic Turing machines in polynomial time under weaker uniformity conditions, expanding their computational capabilities.

## Contribution

It introduces a new simulation method for Turing machines using P systems without charges with reduced uniformity and membrane nesting requirements.

## Key findings

- P systems without charges can simulate polynomial-time Turing machines.
- Simulation works under weaker uniformity conditions.
- Potential for embedding into more complex membrane structures.

## Abstract

It is well known that the kind of P systems involved in the definition of the P conjecture is able to solve problems in the complexity class $\mathbf{P}$ by leveraging the uniformity condition. Here we show that these systems are indeed able to simulate deterministic Turing machines 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 in [1] for P systems with charges can be carried out also in this case.