The computational power of timed P systems with active membranes using promoters

Abstract

P systems with active membranes are a class of bioinspired computing models, where the rules are used in the non-deterministic maximally parallel manner. In this paper, first, a new variant of timed P systems with active membranes is proposed, where the application of rules can be regulated by promoters with only two polarizations. Next, we prove that any Turing computable set of numbers can be generated by such a P system in the time-free way. Moreover, we construct a uniform solution to the $\mathcal{SAT}$ problem in the framework of such recognizer timed P systems in polynomial time, and the feasibility and effectiveness of the proposed system is demonstrated by an instance. Compared with the existing methods, the P systems constructed in our work require fewer necessary resources and RS-steps, which show that the solution is effective to NP-complete problem.

Homeostasis tissue-like P systems with cell separation

“…where -Γ = {l, l ′ , l (1) , l (2) , l (3) , l (4) , l (5) , l (6) , l (7) , l (8) |l ∈ H} ∪ {a r |1 ≤ r ≤ m}; -ω 1 = l 0 ; -ω 2 = {l (3) |l ∈ H}; -i out =1; -R is the set of rules, including type (a) and type (b) in HT P CS systems.…”

“…Relative to a membrane system, its theoretical framework primarily includes the following basic ingredients: the membrane structure, multisets of objects (placed in various regions), and rules [2]. In recent years, many new variants have been proposed, which are all Turing universal (i.e., have equivalent computational power to the Turing machine) [4][5][6][7][8][9]. These variants can provide a richer framework for membrane computing.…”

Solving the SAT Problem by Cell-Like P Systems with Channel States and Symport Rules

“…At present, many new variants have been proposed [3][4][5][6][7][8][9], and many variants have been proven Turing universal. In the theoretical research of membrane computing, various computationally hard problems were solved [10][11][12][13][14]. Recently, inspired by membrane computing, Roy et al proposed a new type of neural computing system [15], which will promote the development of membrane computing.…”

Spiking Neural P Systems with Membrane Potentials, Inhibitory Rules, and Anti-Spikes

“…The distributed parallel computing models obtained from the development of membrane computing are membrane systems, also known as P systems, and the study of P systems has been divided into three types according to the cell membrane structure or cell distribution: cell-like P systems, tissue-like P systems, and neural-like P systems. For the theoretical research of membrane computing, three types of P systems have been extended to obtain several universal computational models [ 3 , 4 , 5 , 6 , 7 ], and the computational complexity of extended P systems has been explored [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. For the application research of membrane computing, existing studies have realized the integration of membrane computing with algorithms for applications in robot control [ 21 , 22 ], data modeling, and optimization [ 23 , 24 , 25 , 26 ], algorithms for solving NP problems [ 27 , 28 , 29 ], clustering algorithms [ 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ], and image processing [ 38 , 39 , 40 ].…”