Bosheng Song

Normal Forms for Some Classes of Sequential Spiking Neural P Systems

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes, where each neuron can have several spiking rules and forgetting rules and neurons work in parallel in the sense that each neuron that can fire should fire at each computation step. In this work, we consider SN P systems with the restrictions: 1) systems are simple (resp. almost simple) in the sense that each neuron has only one rule (resp. except for one neuron); 2) at each step the neuron(s) with the maximum number of spikes among the neurons that can spike will fire. These restrictions correspond to that the systems are simple or almost simple and a global view of the whole network makes the systems sequential. The computation power of simple SN P systems and almost simple SN P systems working in the sequential mode induced by maximum spike number is investigated. Specifically, we prove that such systems are Turing universal as both number generating and accepting devices. The results improve the corresponding ones in Theor. Comput. Sci., 410 (2009), 2982-2991.

Flat maximal parallelism in P systems with promoters

In spite of the fact that many ways of using the evolution rules in a P system were already investigated, there is still a case, which we call the flat maximal parallelism, which appeared in several papers, but which deserves a more careful attention: in each step, in each membrane, a maximal set of applicable rules is chosen and each rule in the set is applied exactly once. In this work, flat maximal parallelism is studied for non-cooperating P systems with promoters. Specifically, we prove that non-cooperating P systems with at most one promoter associated with any rule, working in the flat maximally parallel way, are Turing universal (the Turing universality of such P systems is open if they work in the maximally parallel way). Moreover, a uniform solution to the SAT problem is provided by using non-cooperating P systems with promoters and membrane division, working in the flat maximal parallel way.

Efficient solutions to hard computational problems by P systems with symport/antiport rules and membrane division

P systems are computing models inspired by some basic features of biological membranes. In this work, membrane division, which provides a way to obtain an exponential workspace in linear time, is introduced into (cell-like) P systems with communication (symport/antiport) rules, where objects are never modified but they just change their places. The computational efficiency of this kind of P systems is studied. Specifically, we present a (uniform) linear time solution to the NP-complete problem, Subset Sum by using division rules for elementary membranes and communication rules of length at most 3. We further prove that such P system allowing division rules for non-elementary membranes can efficiently solve the PSPACE-complete problem, QSAT in a uniform way.

Membrane fission: A computational complexity perspective

Membrane fission is a process by which a biological membrane is split into two new ones in the manner that the content of the initial membrane is separated and distributed between the new membranes. Inspired by this biological phenomenon, membrane separation rules were considered in membrane computing. In this work, we investigate cell-like P systems with symport/antiport rules and membrane separation rules from a computational complexity perspective. Specifically, we establish a limit on the efficiency of such P systems which use communication rules of length at most two, and we prove the computational efficiency of this kind of models when using communication rules of length at most three. Hence, a sharp borderline between tractability and NP–hardness is provided in terms of the length of communication rules.

Time-free solution to SAT problem by P systems with active membranes and standard cell division rules

P systems are a class of distributed and parallel computing models inspired by the structure and the functioning of a single cell and complexes of cells. The computational efficiency of P systems with active membranes has been investigated widely with the assumption that the application of rules is completed in exactly one time unit. However, in biological facts, different biological processes may take different times to complete, and the execution time of certain biological process could vary because of external uncontrollable conditions. With this biological motivation, in this work, we solve SAT problem by a family of P systems with active membranes in a time-free manner in the sense that the correctness of the solution does not depend on the precise timing of the involved rules. In such a solution, standard cell division rules for elementary membranes are applied: the newly generated membranes have the same label with their parent membrane. This result answers an open problem formulated in Song et al. (Theor Comput Sci 529:61–68, 2014).

Computational efficiency and universality of timed P systems with membrane creation

P systems are a class of distributed parallel computing models inspired by the structure and the functioning of a living cell, where the execution of each rule is completed in exactly one time unit (a global clock is assumed). However, in living cells, the execution time of different biological processes is difficult to know precisely and very sensitive to environmental factors that might be hard to control. Inspired from this biological motivation, in this work, timed polarization P systems with membrane creation are introduced and their computational efficiency and universality are investigated. Specifically, we give a time-free semi-uniform solution to the SAT problem by a family of P systems with membrane creation in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules. We also prove that time-free P systems with membrane creation are computationally universal.

An efficient time-free solution to SAT problem by P systems with proteins on membranes

The notion of time-free solution to decision problem by P systems with proteins on membranes, in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules, is defined.A time-free uniform solution to the SAT problem by P systems with proteins on membranes is given. P systems with proteins on membranes are a class of bio-inspired computing models, where the execution of each rule completes in exactly one time unit. However, in living cells, the execution time of biochemical reactions is difficult to know precisely because of various uncontrollable factors. In this work, we present a time-free uniform solution to SAT problem by P systems with proteins on membranes in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules, and the P systems are constructed from the sizes of instances.

Tissue P Systems With Channel States Working in the Flat Maximally Parallel Way

Tissue P systems with channel states are a class of bio-inspired parallel computational models, where rules are used in a sequential manner (on each channel, at most one rule can be used at each step). In this work, tissue P systems with channel states working in a flat maximally parallel way are considered, where at each step, on each channel, a maximal set of applicable rules that pass from a given state to a unique next state, is chosen and each rule in the set is applied once. The computational power of such P systems is investigated. Specifically, it is proved that tissue P systems with channel states and antiport rules of length two are able to compute Parikh sets of finite languages, and such P systems with one cell and noncooperative symport rules can compute at least all Parikh sets of matrix languages. Some Turing universality results are also provided. Moreover, the NP-complete problem SAT is solved by tissue P systems with channel states, cell division and noncooperative symport rules working in the flat maximally parallel way; nevertheless, if channel states are not used, then such P systems working in the flat maximally parallel way can solve only tractable problems. These results show that channel states provide a frontier of tractability between efficiency and non-efficiency in the framework of tissue P systems with cell division (assuming P ≠ NP).

Cell-Like P Systems With Channel States and Symport/Antiport Rules

Cell-like P systems with symport/antiport rules are inspired by the structure of a cell and the way of communicating substances through membrane channels between neighboring regions. In this work, channel states are introduced into cell-like P systems with symport/antiport rules, and we call this variant of communication P systems as cell-like P systems with channel states and symport/antiport rules. In such P systems, at most one channel is established between neighboring regions, each channel associates with one state in order to control communication at each step, and rules are used in a sequential manner: on each channel at most one rule can be used at each step. The computational power of such P systems is investigated. Specifically, we show that cell-like P systems with two states and using uniport rules, or with any number of states and using antiport rules of length two, are able to compute only finite sets of non-negative integers. We further prove that cell-like P systems with two membranes are as powerful as Turing machines when channel states and symport/antiport rules are suitably combined. The results show that channel states are a feature that can increase the computational power of cell-like P systems with symport/antiport rules.Cell-like P systems with symport/antiport rules are inspired by the structure of a cell and the way of communicating substances through membrane channels between neighboring regions. In this work, channel states are introduced into cell-like P systems with symport/antiport rules, and we call this variant of communication P systems as cell-like P systems with channel states and symport/antiport rules. In such P systems, at most one channel is established between neighboring regions, each channel associates with one state in order to control communication at each step, and rules are used in a sequential manner: on each channel at most one rule can be used at each step. The computational power of such P systems is investigated. Specifically, we show that cell-like P systems with two states and using uniport rules, or with any number of states and using antiport rules of length two, are able to compute only finite sets of non-negative integers. We further prove that cell-like P systems with two membranes are as powerful as Turing machines when channel states and symport/antiport rules are suitably combined. The results show that channel states are a feature that can increase the computational power of cell-like P systems with symport/antiport rules.

Tissue P Systems with Protein on Cells

Tissue P systems are a class of distributed parallel computing devices inspired by bio- chemical interactions between cells in a tissue-like arran gement, where objects can be exchanged by means of communication channels. In this work, inspired by the biological facts that the movement of most objects through communication channels is controlled by proteins and proteins can move through lipid bilayers between cells (if these cells are fus ed), we present a new class of variant tissue P systems, called tissue P systems with protein on cells, where multisets of objects (maybe empty), together with proteins between cells are exchanged. The computational power of such P systems is studied. Specifically, an efficient (uniform) solution to the SAT problem by using such P systems with cell division is presented. We also prove that any Turing computable set of numbers can be generated by a tissue P system with protein on cells. Both of these two results are obtained by such P systems with communication rules of length at most 4 (the length of a communication rule is the total number of objects and proteins involved in that rule).