Computing with energy and chemical reactions

Taking inspiration from some laws of Nature—energy transformation and chemical reactions—we consider two different paradigms of computation in the framework of Membrane Computing. We first study the computational power of energy-based P systems, a model of membrane systems where a fixed amount of energy is associated with each object and the rules transform objects by manipulating their energy. We show that if we assign local priorities to the rules, then energy-based P systems are as powerful as Turing machines; otherwise, they can be simulated by vector addition systems, and hence are not universal. Then, we consider stochastic membrane systems where computations are performed through chemical networks. We show how molecular species and chemical reactions can be used to describe and simulate the functioning of Fredkin gates and circuits. We conclude the paper with some research topics related to computing with energy-based P systems and with chemical reactions.     

One-membrane symport with few extra symbols

Membrane systems (with symbol objects) are formal models of distributed parallel multiset processing. Symport rules move multiple objects to a neighbouring region. It is known that for P systems with symport rules of weight at most 3 and a single membrane, seven superfluous symbols are enough for computational completeness, and one is necessary. We present the improvements of the lower bounds on the generative power of P systems with symport of weight bounded by 3 and 4, in particular, establishing that six and two extra symbols suffice, respectively. Besides maximally parallel P systems, we also consider sequential ones. In fact, all presented non-universality lower bound results, together with all upper bound results, hold also in this case, yielding the current state of the art.     

P systems with energy accounting ∗

We consider P systems where each evolution rule “Produces” or “Consumes” some quantity of energy, in amounts which are expressed as integer numbers. In each moment and in each membrane the total energy involved in an evolution step should be positive, but if “Soo much” energy is present in a membrane, then the membrane will be destroyed (dissolved). We show that this feature is rather powerful. In the case of multisets of symbol-objects we find that systems with two membranes and arbitrary energy associated with rules, or with arbitrarily many membranes and a bounded energy associated with rules characterize the recursively enumerable sets of vectors of natural numbers (catalysts and priorities are used). In the case of string-objects we have only proved that the recursively enumerable languages can be generated by systems with arbitrarily many membranes and bounded energy; when bounding the number of membranes and leaving free the quantity of energy associated with each rule we have only generated all matrix languages. Several research topics are also pointed out.     

基于能量的受迫哈密顿系统的镇定及在电力系统中的应用

有两个目的,第一目的是考虑电力系统的励磁镇定。将该系统表示为具有耗散的受迫哈密顿系统的形式,随后基于能量构造了李雅普诺夫函数来考察受迫系统的稳定性。第二个目的是提出广义哈密顿系统的模型,广义哈密顿系统具有外部能量供给、内部能量供给及能量消耗,状态空间被描述成具有二次张量场的流形,得到了广义哈密顿系统与坐标无关的全局模型。     

Counterexamples in infinitary rewriting with non-fully-extended rules

We show counterexamples exist to confluence modulo hypercollapsing subterms, fair normalisation, and the normal form property in orthogonal infinitary higher-order rewriting with non-fully-extended rules. This sets these systems apart from both fully-extended and finite systems, where no such counterexamples are possible.     

Minimization strategies for maximally parallel multiset rewriting systems

Maximally parallel multiset rewriting systems (MPMRS) give a convenient way to express relations between unstructured objects. The functioning of various computational devices may be expressed in terms of MPMRS (e.g., register machines and many variants of P systems). In particular, this means that MPMRS are Turing universal; however, a direct translation leads to quite a large number of rules. Like for other classes of computationally complete devices, there is a challenge to find a universal system having the smallest number of rules. In this article we present different rule minimization strategies for MPMRS based on encodings and structural transformations. We apply these strategies to the translation of a small universal register machine (Korec (1996) [9]) and we show that there exists a universal MPMRS with 23 rules. Since MPMRS are identical to a restricted variant of P systems with antiport rules, the results we obtained improve previously known results on the number of rules for those systems.     

P Systems with Mobile Membranes

P systems with active membranes are among the central ones in membrane computing, and they were shown to be both computationally universal (able to simulate Turing machines) and computationally efficient (able to solve hard problems in polynomial time). However, in all cases, these results were obtained by making use of several powerful features, such as membrane polarization, label changing, division of non-elementary membranes, priorities, or cooperative rules. This paper contributes to the research effort of introducing a class of P systems with active membranes having none of the features mentioned above, but still preserving the power and the efficiency. The additional feature we consider instead are the operations of endocytosis and exocytosis: moving a membrane inside a neighboring membrane, or outside the membrane where it is placed. We investigate the power and the efficiency of these systems (also using membrane division) by first proving that they can simulate (with a linear slowdown and without introducing non-determinism) rewriting P systems with 2-replication, for which the universality and the possibility of solving NP-complete problems in polynomial time are known. In this way, the universality and efficiency are also obtained for our systems. We also give a direct and simple proof for the universality result – without using division rules (the proof uses nine membranes, but we do not know whether this number can be decreased).     

Small universal simple spiking neural P systems with weights

Spiking neural P systems with weights（WSN P systems,for short） are a new variant of spiking neural P systems,where the rules of a neuron are enabled when the potential of that neuron equals a given value.It is known that WSN P systems are universal by simulating register machines. However,in these universal systems,no bound is considered on the number of neurons and rules. In this work,a restricted variant of WSN P systems is considered,called simple WSN P systems,where each neuron has only one rule. The complexity parameter,the number of neurons,to construct a universal simple WSN P system is investigated. It is proved that there is a universal simple WSN P system with 48 neurons for computing functions; as generator of sets of numbers,there is an almost simple（that is,each neuron has only one rule except that one neuron has two rules） and universal WSN P system with 45 neurons.     

Membrane systems with carriers

A membrane system is a model of computation which is inspired by some basic features of biological membranes. In this paper we consider another biologically inspired notion, viz., the notion of a carrier (or vehicle), as, e.g., used in gene cloning. We investigate the power of membrane systems where the rules for the evolving of objects are replaced by the rules that carry objects (by vehicles) through membranes. It turns out that these systems (even with a small number of membranes, a small number of carriers, and a small number of passengers taken by carriers) are computationally universal.     

P systems with minimal parallelism

A current research topic in membrane computing is to find more realistic P systems from a biological point of view, and one target in this respect is to relax the condition of using the rules in a maximally parallel way. We contribute in this paper to this issue by considering the minimal parallelism of using the rules: if at least a rule from a set of rules associated with a membrane or a region can be used, then at least one rule from that membrane or region must be used, without any other restriction (e.g., more rules can be used, but we do not care how many). Weak as it might look, this minimal parallelism still leads to universality. We first prove this for the case of symport/antiport rules. The result is obtained both for generating and accepting P systems, in the latter case also for systems working deterministically. Then, we consider P systems with active membranes, and again the usual results are obtained: universality and the possibility to solve NP-complete problems in polynomial time (by trading space for time).     

Spiking neural P systems with extended rules: universality and languages

We consider spiking neural P systems with rules allowed to introduce zero, one, or more spikes at the same time. The motivation comes both from constructing small universal systems and from generating strings; previous results from these areas are briefly recalled. Then, the computing power of the obtained systems is investigated, when considering them as number generating and as language generating devices. In the first case, a simpler proof of universality is obtained, while in the latter case we find characterizations of finite and recursively enumerable languages (without using any squeezing mechanism, as it was necessary in the case of standard rules). The relationships with regular languages are also investigated.     

脉冲神经膜系统在穷举使用规则下产生的二进制字符串语言

脉冲神经膜系统是基于大脑中神经元之间通过突触相瓦协作、处理脉冲的生物现象提出的一种新的模型,文中在穷举使用规则的情况下考虑将脉冲神经膜系统作为串语言产生器:当输出神经元发送出一个或多个神经脉冲时,用数字1表示,否则用数字0表示,当计算停止时,把产生的二进制串定义为系统的计算结果.在文中,作者让明了在穷举使用规则的情况下,具有一个神经元的脉冲神经膜系统可以刻画二进制有限语言,并且证明了在不限制神经元个数的情况下,该系统可以刻画递归可枚举语言.     

Spiking neural P systems: An improved normal form

Spiking neural P systems (in short, SN P systems) are computing devices based on the way the neurons communicate through electrical impulses (spikes). These systems involve various ingredients; among them, we mention forgetting rules and the delay in firing rules. However, it is known that the universality can be obtained without using these two features. In this paper we improve this result in two respects: (i) each neuron contains at most two rules (which is optimal for systems used in the generative mode), and (ii) the rules in the neurons using two rules have the same regular expression which controls their firing. This result answers a problem left open in the literature, and, in this context, an incompleteness in some previous proofs related to the elimination of forgetting rules is removed. Moreover, this result shows a somewhat surprising uniformity of the neurons in the SN P systems able to simulate Turing machines, which is both of a theoretical interest and it seems to correspond to a biological reality. When a bound is imposed on the number of spikes present in a neuron at any step of a computation (such SN P systems are called finite), two surprising results are obtained. First, a characterization of finite sets of numbers is obtained in the generative case (this contrasts the case of other classes of SN P systems, where characterizations of semilinear sets of numbers are obtained for finite SN P systems). Second, the accepting case is strictly more powerful than the generative one: all finite sets and also certain arithmetical progressions can be accepted. A precise characterization of the power of accepting finite SN P systems without forgetting rules and delay remains to be found.     

Tissue P systems with channel states

We consider tissue-like P systems with states associated with the links (we call them synapses) between cells, controlling the passage of objects across the links. We investigate the computing power of such devices for the case of using—in a sequential manner—antiport rules of small weights. Systems with two cells are proved to be universal when having arbitrarily many states and minimal antiport rules, or one state and antiport rules of weight two. Also the systems with arbitrarily many cells, three states, and minimal antiport rules are universal. In contrast, the systems with one cell and any number of states and rules of any weight only compute Parikh sets of matrix languages (generated by matrix grammars without appearance checking); characterizations of Parikh images of matrix languages are obtained for such one-cell systems with antiport rules of a reduced weight.     

Cell communication in tissue P systems: universality results

We introduce an evolution-communication model for tissue P systems where communication rules are inspired by the general mechanism of cell communication based on signals and receptors: a multiset can enter a cell only in the presence of another multiset. Some basic variants of this model are also considered where communication is restricted either to be unidirectional or to use special multisets of objects called receptors. The universality for all these variants of tissue P systems is then proved by using two cells (three cells in the case of unidirectional communication) and rules of a minimal size.     

P Automata with membrane channels

We investigated a variant of purely communicating P systems that are able to accept multisets or even strings given as sequences of terminal symbols taken from the environment. We showed that such P automata with membrane channels equipped with only one membrane and specific activating and prohibiting rules can already recognize any recursively enumerable language of multisets and strings, respectively. Moreover, using only activating rules of a very special kind, we obtained a characterization of regular languages. This work was presented, in part, at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24#x2013;26, 2003.     

A characterization of (regular) circular languages generated by monotone complete splicing systems

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for monotone complete systems, which are finite circular splicing systems with rules of a simpler form. We show that a circular language L is generated by a monotone complete system if and only if the set Lin(L) of all words corresponding to L is a pure unitary language generated by a set closed under the conjugacy relation. The class of pure unitary languages was introduced by A. Ehrenfeucht, D. Haussler, G. Rozenberg in 1983, as a subclass of the class of context-free languages, together with a characterization of regular pure unitary languages by means of a decidable property. As a direct consequence, we characterize (regular) circular languages generated by monotone complete systems. We can also decide whether the language generated by a monotone complete system is regular. Finally, we point out that monotone complete systems have the same computational power as finite simple systems, an easy type of circular splicing system defined in the literature from the very beginning, when only one rule of a specific type is allowed. From our results on monotone complete systems, it follows that finite simple systems generate a class of languages containing non-regular languages, showing the incorrectness of a longstanding result on simple systems.     

Homogeneous spiking neural P systems working in sequential mode induced by maximum spike number

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired by the way neurons communicate by means of spikes, where neurons work in parallel in the sense that each neuron that can fire should fire at each computation step, and neurons can be different in the sense that they can have different sets of spiking rules. In this work, we consider SN P systems with the restrictions: (1) all neurons are homogeneous in the sense that each neuron has the same set of rules; (2) at each step the neuron with the maximum number of spikes among the neurons that are active (can spike) will fire. These restrictions correspond to the fact that the system consists of only one kind of neurons and a global view of the whole network makes the system sequential. The computation power of homogeneous SN P systems working in the sequential mode induced by the maximum spike number is investigated. Specifically, it is proved that such systems are universal as both generating and accepting devices.     

From Watson-Crick L systems to Darwinian P systems

Watson-Crick L systems are language generating devices making use ofWatson-Crick complementarity, a fundamental concept of DNA computing.These devices are Lindenmayer systems enriched with a trigger forcomplementarity transition: if a ``bad' string is obtained, then thederivation continues with its complement which is always a ``good'string. Membrane systems or P systems are distributed parallel computingmodels which were abstracted from the structure and the way offunctioning of living cells. In this paper, we first interpret theresults known about the computational completeness of Watson-Crick E0Lsystems in terms of membrane systems, then we introduce a related way ofcontrolling the evolution in P systems, by using the triggers not in theoperational manner (i.e., turning to the complement in a ``bad'configuration), but in a ``Darwinian' sense: if a ``bad' configurationis reached, then the system ``dies', that is, no result is obtained.The triggers (actually, the checkers) are given as finite state multisetautomata. We investigate the computational power of these P systems.Their computational completeness is proved, even for systems withnon-cooperative rules, working in the non-synchronized way, andcontrolled by only two finite state checkers; if the systems work in thesynchronized mode, then one checker for each system suffices to obtainthe computational completeness.