13th International Conference on Membrane Computing - MTA Sztaki

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Yu. Rogozhin this obstacle and to generate all recursively enumerable languages. An overview of such mechanisms can be found in [16]. One of the goals of this work is to present several of small size universal systems based on splicing. Like in [29, 5] we consider the number of rules as a measure of the size of the system. This approach is coherent with investigations related to small universal Turing machines, e.g. [28]. One of the first ideas to increase the computational power of splicing systems is to consider them in a distributed framework. Such a framework introduces test tubes, corresponding to H systems, which are arranged in a communicating network. The computation is then performed as a repeated sequence of two steps: computation and communication. During the computational step, each test tube evolves as an ordinary H system in an independent manner. During the communication step, the words at each test tube are redistributed among other tubes according to some communication protocol. Test tube systems based on splicing, introduced in [8], communicate through redistribution of the contents of the test tubes via filters that are simply sets of letters (in a similar way to the separate operation of Lipton-Adleman [11, 1]). These systems, with finite initial contents of the tubes and finite sets of splicing rules associated to each component, are computationally complete, they characterize the family of recursively enumerable languages. The existence of universal splicing test tube distributed systems was obtained on this basis, hence the theoretical proof of the possibility to design universal programmable computers with the structure of such a system. After a series of results, the number of tubes sufficient to achieve this result was established to be 3 [12]. The computational power of splicing test tube systems with two tubes is still an open question. The descriptional complexity for such kind of systems was investigated in [2] where it was shown that there exist universal splicing test tube system with 10 rules. The best known result shows that there exist universal splicing test tube system with 8 rules [6] and this result also is presented in this paper. Another extension of H systems was done using the framework of P systems [23], see also [14] and [24]. In a formal way, splicing P systems can be considered like a graph, whose nodes contain sets of strings and sets of splicing rules. Every rule permits to perform a splicing and to send the result to some other node. Since splicing P systems generate any recursively enumerable language, it is clear that there are universal splicing P systems. Like for small universal Turing machines, we are interested in such universal systems that have a small number of rules. A first result was obtained in [29] where a universal splicing P system with 8 rules was shown. Recently a new construction was presented in [5] for a universal splicing P system with 6 rules. The best known result [6] shows that there exists a universal splicing P system with 5 rules and this result is presented in this paper using an inverse morphism and a weak coding. Notice, that this result (5 rules) is the best known for “classical” approach to construct small universal devices. This result is presented in the paper. Similar investigations for P systems with symbol-objects were done in [9, 7] and the lat- 60
Turing computability and membrane computing ter article constructs a universal antiport P system with 23 rules. This result also is presented in the paper. We also consider a class of H systems which can be viewed as a counterpart of the matrix grammars in the regulated rewriting area. These systems are called double splicing extended H systems [16]. In [6] one obtains an unexpected result: 5 rules are enough for such kind of H systems in order to be universal. The following series of results claim existence of universal devices of very small size is presented in the paper. Thus, there exist the following universal devices: – A double splicing extended H system with 5 rules [6], – An extended splicing test tube system with 3 tubes having 8 rules [6], – An extended splicing test tube system with 2 tubes and two alternating filters, having 10 rules [2], – An extended splicing test tube system with 2 tubes and two-symbol filters having 10 rules [2], – A TVDH system of degree 2 having 15 rules [2], – A TVDH system of degree 1 having 17 rules [2], – A splicing P system having 5 rules [6], – An antiport P system having 23 rules [7]. Acknowledgements The author is grateful to Artiom Alhazov for help, useful discussion and comments. References 1. L. Adleman: molecular computation of solutions to combinatorial problems: Science 226 (1994) 1021–1024. 2. A. Alhazov, M. Kogler, M. Margenstern, Yu. Rogozhin, S. Verlan: Small Universal TVDH and Test Tube Systems. <strong>International</strong> Journal of Foundations of Computer Science 22(1) (2011) 143–154. 3. A. Alhazov, R. Freund, Yu. Rogozhin: Computational Power of Symport/Antiport: History, Advances and Open Problems. Lecture Notes in Computer Science 3850 (2006) 1–30. 4. A. Alhazov, M. Kudlek, Yu. Rogozhin: Nine Universal Circular Post Machines. Computer Science Journal of Moldova vol.10 no.3(30) (2002) 247 – 262. 5. A.Alhazov, Yu. Rogozhin, S. Verlan: A small universal splicing P system. Lecture Notes in Computer Science 6501 (2010) 95–102. 6. A. Alhazov, Yu. Rogozhin, S.Verlan: On Small Universal Splicing Systems. Fundamenta Informaticae (in press). 7. A. Alhazov, S. Verlan: Minimization strategies for maximally parallel multiset rewriting systems. TUCS Report No. 862 (2008), and arXiv:1009.2706v1 [cs.FL] and Theoretical Computer Science 412(17) (2011) 1581–1591. 8. E. Csuhaj-Varjú, L. Kari and Gh. Păun: Test tube distributed systems based on splicing. Computers and Artificial Intelligence 15(2–3) (1996) 211–232. 9. E. Csuhaj-Varjú, M. Margenstern, Gy. Vaszil, S. Verlan: Small Computationally Complete Symport/Antiport P systems. Theoretical Computer Science 372(2-3) (2007) 152–164. 61
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Erzsébet Csuhaj-Varjú Marian Gheo
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Editors Erzsébet Csuhaj-Varjú Dep
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Preface In addition to the texts or
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Contents M.A. Martínez-del-Amor, I
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A. Alhazov, Yu. Rogozhin With coope
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A. Alhazov, Yu. Rogozhin 2.3 P Syst
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A. Alhazov, Yu. Rogozhin Such a sys
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A. Alhazov, Yu. Rogozhin applied, f
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A. Alhazov, Yu. Rogozhin - one extr
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B. Aman, G. Ciobanu formalisms is e
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B. Aman, G. Ciobanu membranes appea
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B. Aman, G. Ciobanu • [ ] recep r
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B. Aman, G. Ciobanu Definition 3. A
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B. Aman, G. Ciobanu { w i , for all
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B. Aman, G. Ciobanu The four transi
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B. Aman, G. Ciobanu A state space i
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B. Aman, G. Ciobanu to reiterate th
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On structures and behaviors of spik
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L. Cienciala, L. Ciencialová, M. P
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H. ElGindy, R. Nicolescu, H. Wu pat
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H. ElGindy, R. Nicolescu, H. Wu pro
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H. ElGindy, R. Nicolescu, H. Wu (b)
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H. ElGindy, R. Nicolescu, H. Wu 8 r
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H. ElGindy, R. Nicolescu, H. Wu Pse
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H. ElGindy, R. Nicolescu, H. Wu to
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H. ElGindy, R. Nicolescu, H. Wu ter
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H. ElGindy, R. Nicolescu, H. Wu 4.
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H. ElGindy, R. Nicolescu, H. Wu Tab
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H. ElGindy, R. Nicolescu, H. Wu 6 R
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H. ElGindy, R. Nicolescu, H. Wu (wh
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A formal framework for P systems wi
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A new approach for solving SAT by P
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Maintenance of chronobiological inf
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4 3.5 3 2.5 2 1.5 1 0.5 0 0 50 100
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Using a kernel P system to solve th
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Spiking neural P systems with funct
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L.F. Macías-Ramos, M.J. Pérez-Jim
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Membranes with local environments A
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Membranes with local environments T
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Membranes with local environments -
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Membranes with local environments -
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Membranes with local environments I
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On efficient algorithms for SAT dis
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On efficient algorithms for SAT 2 S
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On efficient algorithms for SAT 2.4
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On efficient algorithms for SAT inc
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On efficient algorithms for SAT •
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On efficient algorithms for SAT Not
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On efficient algorithms for SAT the
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On efficient algorithms for SAT 32.
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A. Obtu̷lowicz - its underlying tr
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A. Obtu̷lowicz 2−ramification
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A. Obtu̷lowicz The correctness of
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An analysis of correlative and quan
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Sublinear-space P systems with acti
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Modelling ecological systems with t
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D. Sburlan assuming that M is in a
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D. Sburlan q 1 {t−, T 1 ↓, T 2
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D. Sburlan We introduced a formal s
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P. Sosík [9, 10], several research
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P. Sosík The rules of a system lik
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P. Sosík 1. The family Π is polyn
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P. Sosík (a) subsequently and recu
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P. Sosík contentFinal = content(l,
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P. Sosík Hence, with the aid of th
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P. Sosík 8. Lakshmanan K. and Rama
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S. Verlan, J. Quiros more relevance
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S. Verlan, J. Quiros For a regular
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S. Verlan, J. Quiros digital FPGA c
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S. Verlan, J. Quiros where k j = N
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S. Verlan, J. Quiros Now let us con
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S. Verlan, J. Quiros We consider a
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S. Verlan, J. Quiros the present co
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S. Verlan, J. Quiros Table 2 gives
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S. Verlan, J. Quiros Using similar
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S. Verlan, J. Quiros 5. M. Maliţa,
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Simplifying Event-B models of P sys
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Author Index Adorna H., 143 Agrigor
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