Figure 2 - available from: Natural Computing
This content is subject to copyright. Terms and conditions apply.
Two successive Turing machine configurations, and the configurations of the P system simulating the transition step (in left-to-right, top-to-bottom order)
Source publication
We investigate the influence that the flow of information in membrane systems has on their computational complexity. In particular, we analyse the behaviour of P systems with active membranes where communication only happens from a membrane towards its parent, and never in the opposite direction. We prove that these “monodirectional P systems” are,...
Similar publications
In this paper, we define transcendental polynomial invariants for two-component virtual string links. One of these invariants is a strictly refinement of the linking polynomial in [M. Xu and H. Gao, Linking polynomials of virtual string links, Sci. China Math. 61(7) (2018) 1287-1302]. It is a homotopy invariant and can distinguish some virtual stri...
Citations
... By restricting communication in only one direction (from the inside to the outside, i.e., membranes can send out molecules but never absorb them), similarly to the restriction on expanding cellular automata, the efficiency of membrane systems decreases and we obtain a characterisation of P NP in polynomial time [6]. This is the class of problems solved in polynomial time by deterministic Turing machines with access to an oracle for an NP problem; this can also be viewed as the class of problems Cook-reducible to NP, which highlights the similarity with expanding cellular automata even more. ...
Many unconventional computing models, including some that appear to be quite different from traditional ones such as Turing machines, happen to characterise either the complexity class P or PSPACE when working in deterministic polynomial time (and in the maximally parallel way, where this applies). We discuss variants of cellular automata and membrane systems that escape this dichotomy and characterise intermediate complexity classes, usually defined in terms of Turing machines with oracles, as well as some possible reasons why this happens.
... 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. ...
... 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. ...
... i } {l (5) i , l ...
P systems are distributed, parallel biological computing models. Tissue P systems are an important variant of membrane computing model, where the environment can provide powerful energy support for cells. Hence, the environment plays a critical role. Nevertheless, in actual biological tissues, there exists a peculiar biological phenomenon called "homeostasis"; that is, the internal organisms maintain stable, thereby reducing their dependence on external conditions (i.e., the environment). In this work, considering cell separation, we construct a novel variant to simulate the mechanism of biological homeostasis, called homeostasis tissue-like P systems with cell separation. In this variant, objects in the environment are finite, and certain energy changes occur inside the cells; moreover, an exponential workspace can be obtained with cell separation in feasible time. The computational power of this model is studied by simulating register machines, and the results show that the variant is Turing universal as number computing devices. Furthermore, to explore the computational efficiency of the model, we use the variant to solve a classic NP-complete problem, the SAT problem, obtaining a uniform solution with a rule length of at most 3.
... The presence of simple cooperation rules, like the ones provided by antimatter, where two opposite objects can annihilate each other, allows the systems to reach # with a shallow membrane structure, also when the systems have no charges [7]. Even when the communication is severely restricted, as in monodirectional systems [5], where send-in is forbidden, uniform families of P systems with active membranes with charges characterize or, if shallow, the class ∥ , as shown in [5]. It is interesting to see that this is not the case for monodirectional systems with antimatter: the additional cooperation provided by object annihilation makes it possible to perform a counting operation once (in a destructive way), thus providing families of this kind of systems the ability to solve all problems in # where only one oracle query suffices, even with only one level of nesting [7]. ...
... The presence of simple cooperation rules, like the ones provided by antimatter, where two opposite objects can annihilate each other, allows the systems to reach # with a shallow membrane structure, also when the systems have no charges [7]. Even when the communication is severely restricted, as in monodirectional systems [5], where send-in is forbidden, uniform families of P systems with active membranes with charges characterize or, if shallow, the class ∥ , as shown in [5]. It is interesting to see that this is not the case for monodirectional systems with antimatter: the additional cooperation provided by object annihilation makes it possible to perform a counting operation once (in a destructive way), thus providing families of this kind of systems the ability to solve all problems in # where only one oracle query suffices, even with only one level of nesting [7]. ...
Many variants of P systems with active membranes are able to solve traditionally intractable problems. Sometimes they also characterize well known complexity classes, depending upon the computational features they use. In this paper we continue the investigation of the importance of (minimal) cooperative rules to increase the computational power of P systems. In particular, we prove that monodirectional shallow chargeless P systems with active membranes and minimal cooperation working in polynomial time precisely characterise P‖#P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{P }^{\#{\mathbf{P }}}_{\parallel }$$\end{document}, the complexity class of problems solved in polynomial time by deterministic Turing machines with a polynomial number of parallel queries to an oracle for a counting problem.
... To simulate cell proliferation in biology, some methods have been proposed, such as membrane division [14]- [16], membrane creation [17], and membrane separation [18]- [20]. Recently, many new variants of P systems have been proposed [21]- [24]. Under the framework of P systems, arithmetic operations [25], [26], logical expressions [27] and linear equations [28] have been solved theoretically. ...
... Based on the model in [40], a new model with no environment has been proposed to solve 3-coloring problem [41]. Recently, inspired by the literature [24], in a tissue P system, the communication between two regions only occurs in one direction, thereby constructing a new variant of tissue P systems [42]. ...
Tissue P systems provide distributed parallel devices inspired by actual biological reality, where communication rules are used for object exchange between cells (or between cells and the environment). In such systems, the environment continuously provides energy to cells, so the cells are very dependent on the objects in the environment. In biology, there is a mechanism called homeostasis, that is, an internal organism is independent from the external conditions, thus keeping itself relatively stable. Inspired by this biological fact, in this paper, we assume that the environment no longer provides energy for cells, introducing multiset rewriting rules into tissue P systems, thereby constructing a novel computational model called homeostasis tissue-like P systems. Based on the model, we construct two uniform solutions in feasible time. One solution is constructed to solve the 3-coloring problem in linear time in standard time, and the other solution is constructed to solve the SAT problem with communication rules and multiset rewriting rules of the length at most 3 in time-free mode. Moreover, we prove that the constructed system can generate any Turing computable set of numbers using communication rules and multiset rewriting rules with a maximal length 3, working in the mode of standard time and time-free, respectively. The results show that our constructed system does not rely on the environment and reflects the phenomenon of biological homeostasis. In addition, although the system runs in time-free way, it not only has Turing university, but also can effectively solve NP-complete problem.
... Inspired by the biological fact that the movement of molecules across a membrane is transported from high to low concentration, an interesting restricting condition called ''monodirectional" [18] was considered in P systems with active membranes, where in such monodirectional P systems, for two given regions, communication only happens in one direction at any computation step, and never in the opposite direction (for more information about P systems with active membranes, one can refer to [4,10,12,39]). In [18], the issue of complexity for monodirectional P systems with active membranes was studied, result shown that families cell-like P systems with monodirectional communication characterize decision problems that are defined by Turing machines with NP oracles. ...
... Inspired by the biological fact that the movement of molecules across a membrane is transported from high to low concentration, an interesting restricting condition called ''monodirectional" [18] was considered in P systems with active membranes, where in such monodirectional P systems, for two given regions, communication only happens in one direction at any computation step, and never in the opposite direction (for more information about P systems with active membranes, one can refer to [4,10,12,39]). In [18], the issue of complexity for monodirectional P systems with active membranes was studied, result shown that families cell-like P systems with monodirectional communication characterize decision problems that are defined by Turing machines with NP oracles. ...
Tissue P systems with channel states are non-deterministic bio-inspired computing devices that evolve by the interchange of objects among regions, determined by the existence of some special objects on channels called states. However, in cellular biology, the movement of molecules across a membrane is transported from high to low concentration, inspired by this biological fact, in this paper,h kind of P systems, named monodirectional tissue P systems with channel states, where communication happens between two given regions only in one direction, is considered. We show that monodirectional tissue P systems using two cells are universal if a maximal length 1 for each symport rule and any number of states or a maximal length 2 for each symport rule and 4 states are combined. Universality result is also achieved by monodirectional tissue P systems with 5 states, any number of cells and a maximal length 1 for each symport rule. Besides, computational efficiency of monodirectional tissue P systems is analyzed when cell division rules are incorporated, and a solution to the Boolean satisfiability problem (the SAT problem) is provided by such systems using a maximal length 2 for each symport rule.
... Inspired by the biological fact that the movement of molecules across a membrane is transported from high to low concentration, the notion of "monodirectionality" was first proposed in cell-like P systems (more precisely, P systems with active membranes [29], readers can refer [6], [19], [22], and [39] for more details about P systems with active membranes), where for two given regions, communication happens only in one direction and never in the opposite direction, that is, for two given regions, either object send-in rules or object send-out rules can be used. ...
Tissue
$P$
systems with promoters provide nondeterministic parallel bioinspired devices that evolve by the interchange of objects between regions, determined by the existence of some special objects called
promoters
. However, in cellular biology, the movement of molecules across a membrane is transported from high to low concentration. Inspired by this biological fact, in this article, an interesting type of tissue
$P$
systems, called monodirectional
tissue
$P$
systems with promoters
, where communication happens between two regions only in one direction, is considered. Results show that finite sets of numbers are produced by such
$P$
systems with one cell, using any length of symport rules or with any number of cells, using a maximal length 1 of symport rules, and working in the maximally parallel mode. Monodirectional tissue
$P$
systems are Turing universal with two cells, a maximal length 2, and at most one promoter for each symport rule, and working in the maximally parallel mode or with three cells, a maximal length 1, and at most one promoter for each symport rule, and working in the flat maximally parallel mode. We also prove that monodirectional tissue
$P$
systems with two cells, a maximal length 1, and at most one promoter for each symport rule (under certain restrictive conditions) working in the flat maximally parallel mode characterizes regular sets of natural numbers. Besides, the computational efficiency of monodirectional tissue
$P$
systems with promoters is analyzed when cell division rules are incorporated. Different uniform solutions to the Boolean satisfiability problem (SAT problem) are provided. These results show that with the restrictive condition of “monodirectionality,” monodirectional tissue
$P$
systems with promoters are still computationally powerful. With the powerful computational power, developing membrane algorithms for monodirectional tissue
$P$
systems with promoters is potentially exploitable.
... Membrane computing is a burgeoning branch of natural computing that develops new computation models based on the structure and functioning of living cells [1,2]. Membrane systems (also called P systems) are distributed parallel computation models in membrane computing. ...
Spiking neural P systems are a class of computation models inspired by the biological neural systems, where spikes and spiking rules are in neurons. In this work, we propose a variant of spiking neural P systems, called spiking neural P systems with polarizations and rules on synapses (PSNRS P systems), where spiking rules are placed on synapses and neurons are associated with polarizations used to control the application of such spiking rules. The computation power of PSNRS P systems is investigated. It is proven that PSNRS P systems are Turing universal, both as number generating and accepting devices. Furthermore, a universal PSNRS P system with 151 neurons for computing any Turing computable functions is given. Compared with the case of SN P systems with polarizations but without spiking rules in neurons, less number of neurons are used to construct a universal PSNRS P system.
... It is already known that bidirectional communication is necessary for uniform families of P systems with charges and only one level of membrane nesting, i.e. shallow, to solve problems in P # in polynomial time [1]. With monodirectional communication, only problems in P ∥ can be solved and, even if polynomial depth in the membrane structure is allowed, only P can be reached [3]. There exists, however, an entire spectrum of possibilities between monodirectional and full bidirectional communication; in particular, there are multiple ways of limiting the amount of bidirectional communication, for example by limiting the number of send-in rules that a membrane or its descendants (i.e. the membranes obtained from it by division) might apply during the computation. ...
... We also assume that both M and M ′ have a binary alphabet. This allows us to reuse the same TM simulation described in [3]. ...
... To simulate a TM, we employ the same construction used for monodirectional P systems in [3]. Here, we just briefly recall the inner computing mechanism and the encoding used. ...
Uniform families of shallow P systems with active membranes and charges are known to characterize the complexity class \(\textsc {P}^{\#\textsf {P}}\), since this kind of P systems are able to “count” the number of objects sent out by the dividing membranes. Such a power is absent in monodirectional systems, where no send-in rules are allowed: in this case, only languages in \(\textsc {P}^{\textsf {NP}}_\parallel \) can be recognized. Here, we show that even a tiny amount of communication (namely, allowing only a single send-in per membrane during the computation) is sufficient to achieve the ability to count and solve all problems in the class \(\textsc {P}^{\#\textsf {P}}_\parallel \), where all queries are performed independently.
... In particular, in the confluent case, systems with no nesting characterize [18] whereas, additional nesting gives additional power [2] until reaching when unlimited nesting is allowed [16,17]. In the monodirectional case even unlimited nesting cannot escape , which is conjecturally smaller [3]. Nonconfluent systems, on the other hand, characterize when there are no internal membranes [15] and immediately gain the full power of with only one level of nesting. ...
... We have shown that, differently from confluent P systems, monodirectionality and a restriction on the depth of the system to 1 [3] (or, equivalently, the absence of both dissolution and non-elementary division) do not prevent non-confluent P systems from reaching in polynomial time. It remains open to establish if this upper bound can be extended to membrane structures of higher (non-constant) depth where non-elementary division is allowed. ...
In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-confluence allows them to solve conjecturally harder problems than confluent P systems, thus reaching \(\mathbf{PSPACE }\). Here we show that \(\mathbf{PSPACE }\) is not only a bound, but actually an exact characterization. Therefore, the power endowed by non-confluence to shallow P systems is equal to the power gained by confluent P systems when non-elementary membrane division and polynomial depth are allowed, thus suggesting a connection between the roles of non-confluence and nesting depth.
... In particular, in the confluent case, systems with no nesting characterize P [11] whereas, additional nesting gives additional power [2] until reaching PSPACE when unlimited nesting is allowed [9,10]. In the monodirectional case even unlimited nesting cannot escape P NP , which is conjecturally smaller [3]. Non-confluent systems, on the other hand, characterize NP when there are no internal membranes [8], and immediately gain the full power of PSPACE with only one level of nesting. ...
In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-confluence allows them to solve conjecturally harder problems than confluent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact characterization. Therefore, the power endowed by non-confluence to shallow P systems is equal to the power gained by confluent P systems when non-elementary membrane division and polynomial depth are allowed, thus suggesting a connection between the roles of non-confluence and nesting depth.
