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\title{Membrane Computing Aggregation (MCA): An Upgraded Framework for Transition P-Systems}
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             \author[1]{Alberto  Arteta}

             \author[2]{Luis Fernando  Mingo}

             \author[3]{Nuria  Gomez}

             \author[4]{Yanjun  Zhao}

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\date{\small \em Received: 8 December 2018 Accepted: 2 January 2019 Published: 15 January 2019}

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\begin{abstract}
        


MCA (Membrane computing aggregation is experimental computational frame. It is inspired by the inner properties of membrane cells (Bio-inspired system). It is capable of problem solving activities by maintaining a special, "meaningful" relationship with the internal/external environment, integrating its self-reproduction processes within the information flow of incoming and outgoing signals. Because these problem solving capabilities, MCA admits a crucial evolutionary tuning by mutations and recombination of theoretical genetic "bridges in a so called ?aggregation? process ruled by a hierarchical factor that enclosed those capabilities. Throughout the epigenetic capabilities and the cytoskeleton and cell adhesion functionalities, MCA model gain a complex population dynamics specifics and high scalability. Along its developmental process, it can differentiate into meaningful computational tissues and organs that respond to the conditions of the environment and therefore "solve" the morphogenetic/configurational problem. MCA, above all, represents the potential for a new computational paradigm inspired in the higher level processes of membrane cells, endowed with quasi universal processing capabilities beyond the possibilities of cellular automata of and agent processing models.

\end{abstract}


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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
n spite of all the recent emphasis and advancements in systems biology, synthetic biology, and network science about modelling of gene networks, protein networks, metabolic and signaling networks, etc. some of the most important computational properties of membrane cells have not been grappled and "abstracted" et: scalability, tissular differentiation, and morphogenesis -i.e., the capability to informationally transcend the cellular level and organize higher level information processes by means of heterogeneous populations of membrane cells organized as "computational tissues and organs".\par
Synthetic biology has become extraordinarily active in the manufacture of very simple and robust models and simulations tailored to the realization problems of circuits and modules in vivo, mostly addressed to prokaryotic systems. In the first wave of these studies, very basic elements such as promoters, transcription factors, and repressors were combined to form small modules with specified behaviors. Currently modules include switches, cascades, pulse generators, oscillators, spatial patterns, and logic formulas \hyperref[b50]{(Purnick \& Weiss, 2009)}. The second wave of synthetic biology is integrating basic parts and modules to create systemslevel circuitry. genomes and synthetic life organisms are envisioned, and application-oriented systems are contemplated. Different computational tools and programming abstractions are actively developed (the Registry of Standard Biological Parts; the Growing Point Language GLP; the Origami Shape Language OSL, the PROTO bio programming language, etc. See details at the Open Wetware site). Evolving cell models of prokaryotes have also been addressed \hyperref[b22]{(Cao et al., 2010)}. \hyperref[b18]{(Bashor et al., 2010)}. As some have put, "systems broaden the scope of synthetic biology designing synthetic circuits to operate in reliably in the context of differentiating and morphologically complex membrane cells present unique challenges and opportunities for progress in the field" \hyperref[b38]{(Haynes \& Silver, 2009)}. However, very few synthetic biology researchers do contemplate using systems.\par
In systems biology, a plethora of modelling developments have been built around signaling pathways, cell cycle control, topologies of protein networks, transcriptional networks, etc. There is a relatively well consolidated thinking, in part due to traditional physiology and to systems science and control theory which were at the origins of this new field, of going "from genes to membrane cells to the whole organ" as D. Noble has done for heart models \hyperref[b41]{(Noble, 2002)}. The integration of proteins to organs has also been promoted by bioinformatic-related projects such as the "Physiome Project" \hyperref[b41]{(Hunter et al., 2002)}. Important works have been done in the vicinity of "network science" in order to make sense of gene networks, protein networks, transcription networks, complexes formation, etc. For instance, about how is dynamically or2anized modularity in the yeast proteinprotein interaction network \hyperref[b36]{(Han et al., 2004)}, it was uncovered that two types of "hub" contribute to the organized modularity of the proteome: "party" hubs which interact with their partners simultaneously, and "date" hubs, which bind their different partners at different times and locations (we will see later on the importance of the discussion on "modularity" in the evodevo field). Predictive models of mammalian membrane cells have been described using graph theory, assembling networks and integrative procedures  {\ref (Ma'yan et al., 2005)}. Important systems biology compilations and far-reaching cellular models have been made by \hyperref[b17]{Balazsi et al. (2005)}, Kitano (see in Oda et al., 2004), \hyperref[b44]{Luscombe et al. (2004)}, \hyperref[b40]{Huh et al., (2010)} ...It has to be emphasized that concerning the views advocated in this proposal, most of systems biology works depart from the goal of "abstracting computational power out from systems" and focus instead on "applying computational power to analyze the organization of systems." Notwithstanding the foregoing, studies such as A. Dan chin (2009) on bacteria as computers making computers, and by Ray et al. (2010) on the operating system of bacteria could be considered as forerunners in the former direction.\par
In the science of development (the "evo-devo" discipline) most of the emphasis has been on modularity. What it exactly means in developmental terms is still a matter of controversy \hyperref[b53]{(Schlosser \& Wagner, 2004;}\hyperref[b23]{Carroll, 2005;}\hyperref[b53]{Sprinzak, 2010)}; but undoubtedly modularity refers to the capability of cellular networks to dissociate networked processes at a lower level and to recombine or redeploy them at the higher level of the multicellular organism. Thanks to the cellular signaling system, the genetic switches, the cytoskeleton, and some other topobiological mechanisms \hyperref[b29]{(Edelman, 1988;}\hyperref[b55]{Szathmary, 2001)}, the unitary network of cellular processes integrated into the cell-cycle may be broken down into coherent modules and be performed separately in different membrane cells within differently specialized tissues \hyperref[b47]{(Palmer, 2004)}. This implies a flexible organization for the deployment of biomolecular processing modules, which actually are "cut" differently in each tissue along the developmental process, due also to chromatin remodelling during development (Ho \& Crabtree, 2010). Interestingly, not only differentiation but also morphology becomes an instance of the scalable "modular" processing, throughout the "tensegrity" emergent property and the ontogenetic arrangement of symmetry breakings in a force field. The emergence of cellular bauplans where signaling, force fields, and cytoskeletal mechanical modes conspire together to create but a few basic morphologies for membrane cells, depending also on the populations present, seems to be another important consequence  {\ref (Mojica et al., 2009)}. Interestingly, complex morphologies obtained out from Turing diffusion model have been cogently discussed as a result of cell-to-cell developmental interactions (Kondo \& Miura, 2010) .Currently, the evo-devo field accumulates a considerable mass of biomolecular-or2anizationfacts, poorly conceptualized yet, to be computationally "abstracted" in the perspective of MCA advancement. equations used up to now. Proteins and other biomolecules become molecular "automata" and the aggregate behavior that emerges out from these models is the combinatorial expression of all those automata doing their specific micro-functions \hyperref[b19]{(Blow, 2009)}. This approach shows promise for "evolvable" advancement of network models endowed with the flexible modularity property. It is somehow close to the already mentioned predictive models of mammalian membrane cells that are using graph theory, assembling networks and integrative procedures  {\ref (Mayan et al., 2005)}. New generations of cellular models (of "automata") have been developed too, with powerful data content and with potential for modelling multi-cellular systems in a general way, supporting userfriendly in silicon experimentation and discovery of emergent properties (Amir- \hyperref[b0]{Kroll et al., 2008)}. Under the approach of Artificial Embryology, a developmental system has been obtained by means of cellular automata systems capable of following "rewriting rules" procedures, emulating elementary morphologies and multicellular distributions \hyperref[b32]{(Federici \& Downing, 2006)}.\par
As for the developments in molecular Biocomputing, the idea that bio-molecules (DNA, RNA, proteins) might be used for computing already emerged in the fifties and was reconsidered periodically with more and more arguments which made it more viable. But the definitive confirmation came in 1994 (Adleman, 1994) when L. Adleman successfully accomplished the first experimental close connection between molecular biology and computer science. He described how a small instance of a computationally intractable problem might be solved via a massively parallel random search using molecular biology methods.\par
An important part of this project is focusing on bio-inspired models of computation abstracted from the very complex networks in living systems. Its goal is to investigate several aspects of these models particularly focused on connections between theoretical models and natural (biological) networks. The main topics are:\par
Computational aspects (computational power, structural and description complexity).\par
Application aspects (simulation, physical implementation, experimental results, training issues). This part is intended to be a contribution to both Global Computing (which includes neural networks, cellular automata, etc.) and Bio-inspired Computing (as a part of Natural Computing) a new and interdisciplinary field which lies at the crossroads of mathematics, computer science, molecular biology and linguistics. There are research groups working in similar or connected topics in Europe (Germany, France, Spain, Holland, Hungary, Romania, Moldavia, Finland, Poland, Austria, Italy), USA, Japan, India, China.\par
In the fields closer to computer science and Biocomputing, it has been important the introduction of the agent based approach (as pioneered by W. Fontana and others), which uses sets of rules to define relationships between cellular components substituting for the simple Boolean networks and differential Several new directions of research have been initiated in the last decade: computing devices inspired from the genome evolution \hyperref[b28]{Dassow et al., 2002)}, membrane systems (Nun, 2002) with an explosive development, evolutionary systems based on the behavior of cell populations \hyperref[b16]{(Ardelean et al.,2004)} computing models simulating the process of gene assembly in ciliates \hyperref[b30]{(Ehrenfeucht et al., 2003)}, \hyperref[b33]{(Freund et al., 2002)}, \hyperref[b42]{(Istrail et al., 2007)}, networks of evolutionary processors  {\ref (Manea et al., 2010)}, etc. The joint efforts of biologists and computer scientists led to a new concept, namely the template-guided recombination which seems to offer a "bioware" implementation of the process of gene assembly \hyperref[b15]{(Angeleska et al., 2007)},  {\ref (Presscot et al., 2003)}.\par
Swarm computation is mainly based on the same idea: a swarm is a group of mobile biological organisms wherein each individual communicates with others by acting on its local environment \hyperref[b31]{(Engelbrecht, 2005)}. A computational model based on multiset rewriting is used to simulate the emergence of autocatalytic cycles which are often found in living systems is proposed in (Suzuki\&Tanaka, 1997). The use of X-machines, a variant of finite state machines with much more computational power, is used to model immunological pathways (Holcombe\&Be11,1998). Moreover, \hyperref[b42]{(Istrail et al., 2007)} proposes a new paradigm, "genomic computer", where the entire genomic regulatory system is viewed as a computational system and not only the immune system as it was considered in  {\ref (Dasgupta,1998)}.\par
Many works were devoted to the study of a wide range of operations on biological sequences in vivo and in vitro (bio-operations): PA-matching, annealing, Watson-Crick superposition, transposition, inversion, duplication, translocation, etc.  {\ref (Karp,2002)} gives an overview of the most important and attractive problems for mathematicians coming from genomics and molecular biology. Last but not least, the molecular computing contributed to the understanding of selfassembly which is one of the key concepts in nanoscience  {\ref (Reif\&LaBean,2007)}.\par
The new sub-area of Computation Theory called Bio-Inspired Computing is very dynamic. After approximately 12 years the bibliography about Bio-Inspired Computing counts nearly 1000 papers and several books and grows rapidly each year. These papers were published in either computer science forums or biological ones. Many prestigious international journals hosted special issues but new journals were also created: a permanent column in the  
\section[{II.}]{II.} 
\section[{Membrane Computing}]{Membrane Computing}A Transition P System of degree n 1 > n is a construct ( ) 0 1 1 1 i ) , R ) , . . ( R ( , , . . , , , V n , n , n ? ? ? ? µ = ?\par
Where:\par
V is an alphabet; its elements are called objects; ? is a membrane structure of degree n, with the membranes and the regions labeled in a one-to-one manner with elements in a given set; in this section we always use the labels 1, 2, n;  n i i ? ? ? 1? ? ? ? 2 2 1 1 2 2 2 2 2 2 1 1 2 1 1 1 2 2 1 1 1 1\par
P-systems evolve, which makes it change upon time; therefore, it is a dynamic system. Every time that there is a change on the p-system we will say that the psystem is in a new transition. The step from one transition to another one will be referred to as an evolutionary step, and the set of all evolutionary steps will be named computation. Processes within the psystem will be acting in a massively parallel and nondeterministic manner. (Similar to the way the living cells process and combine information). We will say that the computation has been successful if:III. 
\section[{The Upgrade}]{The Upgrade}\par
The proposal is a new computational paradigm based on Membrane cells, scalable ones which are capable to produce "computational tissues and organs". The organization of such computational tissues and organs is inspired by the emerging informational properties of biomolecular networks and will be based on scalable "membrane cells" guided by functional rules similar to the biological ones (molecular recognition, self-assembly and topo biology-theory rules).\par
The direct inspiration from the membrane cells is precisely the breakthrough of the MCA project. By building computational tissues our proposal makes an evolutionary jump with respect of today research in this field, mainly focused on aggregates of unicellular organisms (e.g. bacteria). Far from modelling and simulating the cellular processes, our computational paradigm will be a clear abstraction of the basic mechanisms and computational capabilities of the membrane cells and tissues, in order to solve complex problems in a new (bioinspired) way.\par
Real tissues display far more complex properties (emergent properties) than the sum of the properties of the individual membrane cells they are made from. In the same way, the emergent properties and functions of our membrane cells and computational tissues will be used for the resolution of real problems, impossible to be appropriately solved by conventional methods: not only biological morphogenesis, but also evolution of economic systems and prediction of crisis, optimization of "industrial ecologies", analysis of the dynamics of social interactions and conflicts, ecosystem disturbances, etc., that are more complex than combinatorial optimization, as well as other classical NP-Complete ones.\par
Our "membrane cells" will be a species of "proto-membrane cells" and a far objective of the project is also the ex-novosynthesis of " membrane cells" and tissues performing as living computational biomolecular networks. The lon2-term vision that motivates this breakthrough is to build new information processing devices with evolving capabilities, which will adapt themselves to the complexity of the problems. In particular, we foresee a synthetic approach to build computational membrane cells and tissues, and to create computational bio-inspired devices of higher complexity (tissues-organs). A far future objective of the project goes beyond the mathematical, software and hardware tools. It is to obtain in lab synthesized "living" information processing systems based on artificial "membrane cells" and hybrid systems combining living components (our "synthesized membrane cells") and non-living elements (e.g. silicon-based).\par
MCA approach is the most appropriate to deal with extremely complex problems that will be crucial in the future. It shows potential to go beyond classical Biocomputing strategies such as self-reproducing machines, cellular automata, perceptron's \& neural networks, genetic algorithms, adaptive computing, bacteria-based computation, artificial membrane cells, etc. Specifically, a new generation of natural computing could be built, based upon the scalable " membrane cells" with problem solving capacity in very different realms: biomaterials and bioengineering, non-linear parallel processing, design of bioinspired systems, modelling of economic, industrial and financial systems, optimization strategies in social settings, etc. For the achievement of our long-term objectives we need to: analyze the wide amount of existing knowledge regarding one of the deepest sources of biocomputational power, the topological and flexible networking properties of biomolecular scalable modules in membrane cells, realize an abstraction of the basic mechanisms and computational capabilities of the membrane cells both at sub cellular and networking level, and develop formal models to be used in new information processing technologies, basically based on combinatory processes of protein domains and genetic switches, together with cytoskeleton dynamics and topobiology-theory, use the above proposed models to create scalable "/proto membrane cells" and abstract-formal "evolvable" cellular networks and computational tissues \& organs endowed with these flexible modularity properties.\par
For our far final objective we need to obtain in lab proof that synthesis of new forms of living" membrane cells" in an inverse process: "membrane cells and tissues" => "theoretical abstract/formal models" => "artificial membrane cells and tissues" => "in lab synthesized living membrane cells" is possible. MCA breakthrou2h is an essential step towards the achievement of our lon2-term vision because it will set the theoretical basis and develop the experimental tools for the creation of the scalable membrane cells, computational tissues and organs (both abstract and living ones). 
\section[{IV.}]{IV.} 
\section[{MCA System}]{MCA System}\par
A MCA is a set ?= \{? 0 , ? 1 , ? 2 , ? , ? ???1 , ? ?? ) and a set ? of aggregation rules among membranes. The set of aggregation rules are not fully integrated with the evolution rules of a given p-System but establishes the correlation between 2 given membrane models by deciding the way 2 or mere P-systems are being aggregated. The rules can be defined as a Matrix relation( ) ? ? ? ? ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? n m m n n n m m m u . . . u u k . . . k k u . . . . . . u . . . u . . . u . . . u u u . . . u u , k , . . , k , k 2 1 2 1 2 1 2 2 2 1 2 1 2 1 1 1 2 1 1\par
Where ?1(k) is the aggregation relation and is defined by the association of n P-systems, k determines the aggregation rules of each component in every psystem Iand Uare the component (objects). Evolution rule application phase.\par
This phase is the one that has been implemented following different techniques.\par
In every region within a p-system, the evolution rules application phase is described as follows:\par
Rules application to a multiset of object in a region is a transforming process of information which has input, output and conditions for making the transformation.\par
Given a region within a p-system, let U=\} n i | a \{ i ? ? 1\par
be the alphabet of objects, m a multiset of objects over U and R(U,T) a multiset of evolution rules with antecedents in U and targets in T.\par
The input in the region is the initial multiset m.\par
The output is a maximal multiset m'.\par
The transformations have been made based on the application of the evolution rules over m until m' is obtained.\par
Application of evolution rules in each region of P systems involves subtracting objects from the initial multiset by using rules antecedents. Rules used are chosen in a non-deterministic manner. This phase ends when no rule is applicable anymore.\par
The transformation only needs rules antecedents as the consequents are part of the communication phase. 
\section[{Observation}]{Observation}\par
Let N k i ? be the number of times that the rule i r is applied. Therefore, the number of symbols j a which have been consumed after applying the evolution rules a specific number of times will be: ? ? ? ? 2 2 1 1 2 2 2 2 2 2 1 1 2 1 1 1 2 2 1 1 1 1\par
Maximal multiset is that one that complies with:? ? m l n i l i m j j i j i u ) u k ( - u 1 1 1 = = = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? [1] [Arteta,2010] V. 
\section[{Correction}]{Correction}\par
The correction of the system fully relies in the correction of the internal P-system of the MCA. In order to prove the aggregation system is distributed then 2 processes need to be proven. 1. Correction of the formal definition of Transition P-System (Paun , 1998) 2. Correction of the aggregation rules applying to 2\par
given P-systems.\par
The correction of the second point gets reduced to a deductive demonstration where the aggregation of 2 given P-systems is base case and the generic case of n-P-systems can be seen as the aggregation of n-1 Psystems (inductive case) with a correct aggregation to the last one.\par
Thus, the key is to prove that aggregation of 2 given P-system is a correct process and indeed reinforce the idea of full inherent parallelism and nondeterministic modelling that membrane models are after.\par
Aggregation rule. Let us use a short definition of a given P-System ( ) The result is the Unionof both. Correctness for this operation is also obvious.0 1 1 1 i ) , R ) , . . (\par
? The aggregation of the 2set of the set of the evolution rules ?? 12 is obvious. The result is the Union of both. Correctness for this operation is also obvious.\par
There are 2 factors in the aggregation that are not obvious which are the aggregated Set of regions ?? 12 . This set of regions is constructed in our proposal as supervised and directed by the factor ? that defines the capabilities previously mentioned. This ? is defined dynamically by the nature of problem the MCA is about to fix. i.e.in a problem of sum of squares is not necessary aggregation as 2 independent P-system could calculate their squares  {\ref [Paun,2001]} and send those outputs to a third (obvious) one that calculates the sum of both results. However, for didactic purposes and aggregated solution could be provided in where a MCA is created with 2 Input P-systems. The aggregated would assign equal ? (priority) to both of them, and then either of them could contain the other one. The container P-system process the output of the contained P-system by adding it to an another square number.\par
? The aggregation of the regions of 2 P-systems would be determined by a priority or hierarchy described by ?. This is a dynamic factor that must be configured right before the problem is dealt with. ? The aggregated P-system will have to work the communication phase after every evolutionary step. This communication phase also fully relies on the hierarchy establish by ? and will operate as normal when the aggregation is complete and the MCA is finished. 
\section[{a) Inductive case}]{a) Inductive case}\par
Given a successful aggregation (MCA) of n P-systems MCA (n), is it correct to aggregate n+1 P-systems?\par
The inductive case is a direct consequence of the aggregated property.\par
MCA (n) system becomes a complex P-System with an aggregation of regions according to the ? factor .MCA (n)= let's call the aggregated P-system as ?? ?? =\{? 1 , ??, ð??"ð??", ??1\}. Once the aggregation is seen as a P-system, aggregating it with another ?? 1 is obvious by applying the base case. 
\section[{b) Simulations and results}]{b) Simulations and results}\par
We have been performing some simulations in simple problem solving in same traditional computing paradigm for small problems clearly aggregation is not necessary, although the advantage of this proposal shows up, when the complexity of the problem increases. Theoretically a fully and corrected aggregated Solution (A whole MCS) would overweight Other problems, especially those that requires sub solutions that are part of optimization techniques would be required to establish a clear hierarchy in the aggregation of MCA. Thus: the cost of the calculation of ? and he redesign of the membrane system that can always occur during compiling time anyways. The analysis is very direct. The simulations are running in the same platform and just focuses in performance time based. All problems are considered simple problems due to the limitations of processing a complex problem with a complex set of aggregation rules which will jeopardize the accuracy of the analysis. Nevertheless, it is indicative to see that there is a variation in the performance when the level of complexity slightly increases which suggest that aggregation can be a good approach when the level of complexity increases. 
\section[{VI.}]{VI.} 
\section[{Conclusions}]{Conclusions}\par
Membrane computing has been growing since George Paun defined it in 1998. Since then new variations have been suggested to try to fit this model to new realities. The main goal for this unconventional paradigm is to improve the performance of the traditional algorithms due to the inherent limitation of the model. Simulations are still a big part of membrane computing and they are useful to extract right conclusions about the new model. In particular, this model is a great candidate to be applied to complex models that require an aggregated solution that is part of other sub solution whole super solutions as long as the defined rules in the MCA are followed. The aggregation factor that is linked to the minimal membrane cells is the component that complement the use membrane computing as a whole and as unite aggregated model. As the creation of this factor generates difficulties because it depends on the nature of the problem, it does not damage the performance during the execution as the factor is calculated in compiling time. New techniques to atomize the generation of ? as this could create a complete dynamic model that fully adjust to the problem and create the right MCA. The necessity of opening the line of research is out of question. The field is growing and new experiments are required. MCA systems are provided as a natural solution to upgrade the nature of membrane computing by not only taking advantage of the properties of the membrane cells but by the way these cells are aggregated. The future work will be involving complex problems in complex aggregated structures, so the analysis can be more relevant. Nevertheless, the evidence points out that aggregation is a natural solution to deal with complex problems that nowadays are being processed by conventional approaches such as backtracking or dynamic programming.\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{11}\includegraphics[]{image-3.png}
\caption{\label{fig_1}, 1 , 1 ,a}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-5.png}
\caption{\label{fig_3}1 Definition}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.2678082191780822\textwidth}P{0.011643835616438355\textwidth}P{0.011643835616438355\textwidth}P{0.011643835616438355\textwidth}P{0.011643835616438355\textwidth}P{0.011643835616438355\textwidth}P{0.011643835616438355\textwidth}P{0.19794520547945205\textwidth}P{0.034931506849315064\textwidth}P{0.2328767123287671\textwidth}P{0.034931506849315064\textwidth}P{0.011643835616438355\textwidth}}
?\tabcellsep =\tabcellsep V\tabcellsep ,\tabcellsep µ\tabcellsep ,\tabcellsep ?\tabcellsep R , . . , ( , n ?\tabcellsep , ?\tabcellsep n\tabcellsep , ?\tabcellsep n\\
\multicolumn{8}{l}{Base case. Given 2}\tabcellsep \tabcellsep \multicolumn{3}{l}{Transition P-system}\\
?? 1\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_0}}\end{figure}
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\end{bibitemlist}
 			 		 	 
\end{document}
