LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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264 Lila Kari, Carlos Martín-Vide, and Andrei Păun Obviously, P systems with minimal symport/antiport rules and using only one membrane can compute at most finite sets of numbers, at most as large as the number of objects present in the system in the initial configuration: the antiport rules do not increase the number of objects present in the system, the same with the symport rules of the form (a, out), while a symport rule of the form (a, in) should have a ∈ V − E (otherwise the computation never stops, because the environment is inexhaustible). The family NOP2(sym1,anti1) contains infinite sets of numbers. Consider, for instance, the system Π =({a, b}, [ 1 [ 2 ] 2 ] 1 ,a,λ,{b},R1,R2, 2), R1 = {(a, out; b, in), (a, in)}, R2 = {(a, in), (b, in)}. After bringing an arbitrary number of copies of b from the environment, the object a gets “hidden” in membrane 2, the output one. An estimation of the size of families NOPm(sym1,anti1) form =2, 3, 4, 5 remains to be found. The P systems with symport and antiport rules are interesting from several points of view: they have a precise biological inspiration, are mathematically elegant, the computation is done only by communication, by moving objects through membranes (hence the conservation law is observed), they are computationally complete. Thus, they deserve further investigations, including from the points of view mentioned above. References 1. B. Alberts, Essential Cell Biology. An Introduction to the Molecular Biology of the Cell, Garland Publ. Inc., New York, London, 1998. 2. F. Bernardini, M. Gheorghe, On the Power of Minimal Symport/Antiport, Workshop on Membrane Computing, Tarragona, 2003. 3. R. Freund, A. Păun, Membrane Systems with Symport/Antiport: Universality Results, in Membrane Computing. Intern. Workshop WMC-CdeA2002, Revised Papers (Gh. Păun, G. Rozenberg, A. Salomaa, C. Zandron, eds.), Lecture Notes in Computer Science, 2597, Springer-Verlag, Berlin, 2003, 270–287. 4. P. Frisco, J.H. Hogeboom, Simulating Counter Automata by P Systems with Symport/Antiport, in Membrane Computing. Intern. Workshop WMC-CdeA2002, Revised Papers (Gh. Păun, G. Rozenberg, A. Salomaa, C. Zandron, eds.), Lecture Notes in Computer Science, 2597, Springer-Verlag, Berlin, 2003, 288–301. 5. J.Hopcroft,J.Ulmann,Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979. 6. C. Martín-Vide, A. Păun, Gh. Păun, On the Power of P Systems with Symport and Antiport Rules, J. of Universal Computer Sci., 8, 2 (2002) 317–331. 7. A. Păun, Gh. Păun, The Power of Communication: P Systems with Symport/Antiport, New Generation Computing, 20, 3 (2002) 295–306. 8. Gh. Păun, Computing with Membranes, J. of Computer and System Sciences, 61, 1 (2000), 108–143, and Turku Center for Computer Science-TUCS Report No 208, 1998 (www.tucs.fi).
On the Universality of P Systems with Minimal Symport/Antiport Rules 265 9. Gh. Păun, Membrane Computing. An Introduction, Springer-Verlag, Berlin, 2002. 10. Gh. Păun, M. Perez-Jimenez, F. Sancho-Caparrini, On the Reachability Problem for P Systems with Symport/Antiport, Proc. Automata and Formal Languages Conf., Debrecen, Hungary, 2002. 11. G. Rozenberg, A. Salomaa, eds., Handbook of Formal Languages, 3 volumes, Springer-Verlag, Berlin, 1997.
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Lecture Notes in Computer Science 2
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Nata˘sa Jonoska Gheorghe Păun Grz
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Thomas J. Head
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VIII Preface portant to keep in min
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X Table of Contents Formal Properti
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Solving Graph Problems by P Systems
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where Solving Graph Problems by P S
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Writing Information into DNA Masano
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Writing Information into DNA 25 Ham
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Writing Information into DNA 27 Fig
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Writing Information into DNA 29 Dea
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5 Results 5.1 DNA Code for the Engl
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Writing Information into DNA 33 3.
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Writing Information into DNA 35 101
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Balance Machines: Computing = Balan
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+ .. . + Balance Machines: Computin
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x Balance Machines: Computing = Bal
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1 Balance Machines: Computing = Bal
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Eilenberg P Systems with Symbol-Obj
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2 Definitions Definition 1. A strea
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5 Conclusions Eilenberg P Systems w
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Molecular Tiling and DNA Self-assem
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3 Molecular Self-assembly Processes
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8 Hierarchical Tiling Molecular Til
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References Molecular Tiling and DNA
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On Some Classes of Splicing Languag
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ˆxa ˆby ✬ ✩✬ ✩ a b x y
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The Power of Networks of Watson-Cri
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Fixed Point Approach to Commutation
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Here the last one holds if and only
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� � � � � Fixed Point App
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Remarks on Relativisations and DNA
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Splicing Test Tube Systems and Thei
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Splicing Test Tube Systems 141 the
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Splicing Test Tube Systems 143 to a
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Splicing Test Tube Systems 145 6. R
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Splicing Test Tube Systems 147 (c)
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I0 Ai i Splicing Test Tube Systems
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Splicing Test Tube Systems 151 4. J
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Digital Information Encoding on DNA
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DNA-based Cryptography Ashish Gehan
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DNA-based Cryptography 169 concern.
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DNA-based Cryptography 171 The one-
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DNA-based Cryptography 173 of DNA t
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DNA-based Cryptography 175 Fig. 3.
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DNA-based Cryptography 177 the comp
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DNA-based Cryptography 179 can be c
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DNA-based Cryptography 181 4.4 DNA-
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DNA-based Cryptography 183 Fig. 7.
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DNA-based Cryptography 185 offer li
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DNA-based Cryptography 187 30. C. M
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Splicing to the Limit Elizabeth Goo
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Splicing to the Limit 191 molecular
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Splicing to the Limit 193 Discussio
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Example 9. The splicing rules are S
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−2α � kNNk = −2αMN, k α
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Finally we define the limit languag
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6 Conclusion Splicing to the Limit
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Formal Properties of Gene Assembly
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(a) (b) Formal Properties of Gene A
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--- ◦ ❄ ⊗ γ ✲ A Proof of R
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A Proof of Regularity for Finite Sp
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The Duality of Patterning in Molecu
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The Duality of Patterning in Molecu
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Membrane Computing: Some Non-standa
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where: Membrane Computing: Some Non
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where: Membrane Computing: Some Non
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The P Versus NP Problem Through Cel
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Realizing Switching Functions Using
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Realizing Switching Functions Using
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AND Gate Realizing Switching Functi
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NOR Gate Realizing Switching Functi
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Plasmids to Solve #3SAT Rani Siromo
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Plasmids to Solve #3SAT 363 A comme
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Plasmids to Solve #3SAT 365 from th
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Communicating Distributed H Systems
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Proof Communicating Distributed H S
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Books: Publications by Thomas J. He
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Publications by Thomas J. Head 387
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Publications by Thomas J. Head 389
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LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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