Cell-Like P Systems with Request Rules and Rules Production/Removal

P systems are natural computing models inspired by the architecture and the function of living cells, which have the maximal parallelism characteristic and can improve computational efficiency. This work constructs a new variant of P systems named cell-like P systems with request rules and rules production/removal, which is also called CRQPR P systems for short. The CRQPR P systems use only request rules requesting objects from the parent membrane of a specific membrane. The skin membrane can request objects from the environment. Moreover, new rules can be produced, and existing rules can be removed during the computation. The Turing universality of CRQPR P systems can be achieved. 1) CRQPR P systems with two membranes using request rules of length at most two or one membrane using request rules of length at most three can compute Turing computable natural numbers. 2) CRQPR P systems with two membranes using request rules of length at most three can compute Turing computable functions.