The model of membrane computing, also known under the name of P systems, is a bio-inspired large-scale parallel computing paradigm having a good potential for the design of massively parallel algorithms. For its implementation it is very natural to choose hardware platforms that have important inherent parallelism, such as field-programmable gate arrays (FPGAs) or compute unified device architecture (CUDA)-enabled graphic processing units (GPUs). This article performs an overview of all existing approaches of hardware implementation in the area of P systems. The quantitative and qualitative attributes of FPGA-based implementations and CUDA-enabled GPU-based simulations are compared to evaluate the two methodologies.

/pdf/an-overview-of-hardware-implementation-of-membrane-computing-2i4hdddy4v.pdf

An Overview of Hardware Implementation of Membrane Computing Models

The issue of reversibility in computational paradigms has gained interest in recent years In this paper we investigate how to reverse steps in membrane systems computations The problem is that computation steps in membrane systems do not preserve all the information that has to be used when reversing them We try to formalize the relevant information needed, and we show that the proposed approach enjoy the so called loop lemma, which basically assures that the undoing obtained by reversely applying rules is correct

Reversing Steps in Membrane Systems Computations

According to the P conjecture by Gh. Paun, polarizationless P systems with active membranes cannot solve $${\mathbf {NP}}$$-complete problems in polynomial time. The conjecture is proved only in special cases yet. In this paper we consider the case where only elementary membrane division and dissolution rules are used and the initial membrane structure consists of one elementary membrane besides the skin membrane. We give a new approach based on the concept of object division polynomials introduced in this paper to simulate certain computations of these P systems. Moreover, we show how to compute efficiently the result of these computations using these polynomials.

/pdf/a-new-method-to-simulate-restricted-variants-of-2jdk1wjd5p.pdf

A new method to simulate restricted variants of polarizationless P systems with active membranes

P systems with active membranes have been widely used to attack problems in $${\mathbf{NP}}$$ or even in $${{\mathbf{PSPACE }}}$$; in general, an exponential amount of space is generated in polynomial time by dividing existing membranes. Natural questions arise in this framework, concerning the power of P systems when different bounds are considered for the use of the space resource. We consider in this paper two natural bounds: the amount of available physical space (in terms of the number of objects and membranes) and the organization of the membrane structure (in particular, concerning the depth of the membrane structure). We present the main results obtained so far on this subject.

Bounding the space in P systems with active membranes

Tissue-like P systems are a type of distributed parallel computing models inspired by actual biological tissue. In this paper, we consider a new variant of tissue-like P systems, which is called tissue-like P systems with evolutional symport/antiport rules. Unlike traditional models of this type, in the new P systems, objects can change during transmission. In biology, an organism that is in “homeostasis” reduces its dependence on external conditions, thereby keeping it relatively constant and maintaining a relatively stable internal environment. In our work, we remove the assumption that the quantity of objects in the environment is infinite, reducing the influence of the environment on this system, so the environment no longer provides powerful energy for cells. Moreover, the time-free mode is introduced into this type of P systems, which makes the constructed systems more robust. We investigate the computational power and computational efficiency of the constructed system. Specifically, by simulating register machines, such a P system can generate any Turing computable set of numbers. In addition, we prove that this constructed system can efficiently solve the $\mathcal {SAT} $ problem. Although we restrict P systems and consider time-free manner, the results show that this system is not only Turing universal, but also can solve NP-complete problem.

/pdf/timed-homeostasis-tissue-like-p-systems-with-evolutional-12ksmsty71.pdf

Timed Homeostasis Tissue-Like P Systems With Evolutional Symport/Antiport Rules

In this paper we give two families of P systems with active membranes that can solve the satisfiability problem of propositional formulas in linear time in the number of propositional variables occurring in the input formula. These solutions do not use polarizations of the membranes or non-elementary membrane division but use separation rules with relabeling. The first solution is a uniform one, but it is not polynomially uniform. The second solution, which is based on the first one, is a polynomially semi-uniform solution.

A new approach for solving SAT by p systems with active membranes

We prove that every single-tape deterministic Turing machine working in $t(n)$ time, for some function $t:\mathbb {N}\rightarrow \mathbb {N}$, can be simulated by a uniform family of polarizationless P systems with active membranes. Moreover, this is done without significant slowdown in the working time. Furthermore, if $\log t(n)$ is space constructible, then the members of the uniform family can be constructed by a family machine that uses $O(\log t(n))$ space.

Simulating Turing Machines with Polarizationless P Systems with Active Membranes

In this paper we consider three restricted variants of P systems with active membranes: (1) P systems using send-out communication rules only, (2) P systems using elementary membrane division and dissolution rules only, and (3) polarizationless P systems using dissolution and unit evolution rules only. We show that every problem in $\mathbf {P}$ can be solved with uniform families of any of these variants using reasonably weak uniformity conditions. This, using known results on the upper bound of the computational power of variants (1) and (3) yields new characterizations of the class $\mathbf {P}$. In the case of variant (2) we provide a further characterization of $\mathbf {P}$ by giving a semantic restriction on the computations of P systems of this variant.

Remarks on the Computational Power of Some Restricted Variants of P Systems with Active Membranes

In this paper we consider three restricted variants of P systems with active membranes: (1) P systems using send-out communication rules only, (2) P systems using elementary membrane division and dissolution rules only, and (3) polarizationless P systems using dissolution and unit evolution rules only We show that every problem in $\mathbf {P}$ can be solved with uniform families of any of these variants using reasonably weak uniformity conditions This, using known results on the upper bound of the computational power of variants (1) and (3) yields new characterizations of the class $\mathbf {P}$ In the case of variant (2) we provide a further characterization of $\mathbf {P}$ by giving a semantic restriction on the computations of P systems of this variant

Gábor Kolonits

Papers

A new method to simulate restricted variants of polarizationless P systems with active membranes

A new approach for solving SAT by p systems with active membranes

Simulating Turing Machines with Polarizationless P Systems with Active Membranes

Remarks on the Computational Power of Some Restricted Variants of P Systems with Active Membranes

Remarks on the Computational Power of Some Restricted Variants of P Systems with Active Membranes