We prove that uniform and semi-uniform families of P systems with active membranes using only communication and nonelementary division rules are not computationally universal. However, they are powerful enough to solve exactly the problems solvable by Turing machines operating in time and space that are ”tetrational” (i.e., bounded by a stack of exponentials of polynomial height) with respect to the size of the input.
Porreca, A., Leporati, A., Zandron, C. (2010). On a Powerful Class of Non-universal P Systems with Active Membranes. In Developments in Language Theory (pp.364-375). Berlino : Springer-Verlag [10.1007/978-3-642-14455-4_33].
On a Powerful Class of Non-universal P Systems with Active Membranes
PORRECA, ANTONIO ENRICO;LEPORATI, ALBERTO OTTAVIO;ZANDRON, CLAUDIO
2010
Abstract
We prove that uniform and semi-uniform families of P systems with active membranes using only communication and nonelementary division rules are not computationally universal. However, they are powerful enough to solve exactly the problems solvable by Turing machines operating in time and space that are ”tetrational” (i.e., bounded by a stack of exponentials of polynomial height) with respect to the size of the input.
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