LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

More documents

Recommendations

Info

342 Mario J. Pérez-Jiménez et al. (when specifying rules, pairs (a, here) are simply written a, the indication here is omitted). For each (a, inj) ∈ v an object a should be moved in the membrane with label j, providing that this membrane is immediately inside membrane i (that is, membrane i is the father of membrane j); if membrane j is not directly accesible from membrane i (that is, if membrane j is not a child membrane of membrane i), then the rule cannot be applied. Finally, if δ appears in v, then membrane i is dissolved; that is, membrane i is removed from the membrane structure, and all objects and membranes previously present in it become elements of the immediately upper membrane (the father membrane) while the evolution rules and the priority relations of the dissolved membrane are removed. The skin membrane is never dissolved; that is, no rule of the form u → v ′ δ is applicable in the skin membrane. All these operations are done in parallel, for all possible applicable rules u → v, for all occurrences of multisets u in the membrane associated with the rules, and for all membranes at the same time. TherulesfromthesetRi, 1≤ i ≤ p, are applied to objects from membrane i synchronously, in a non-deterministic maximally parallel manner; that is, we assign objects to rules, non-deterministically choosing the rules and the objects assigned to each rule, but in such a way that after this assignation no further rule can be applied to the remaining objects. Therefore, a rule can be applied in the same step as many times as the number of copies of objects allows it. On the other hand, we interpret the priority relations between the rules in a strong sense: aruleu→vin a set Ri can be used only if no rule of a higher priority exists in Ri and can be applied at the same time with u → v. A configuration of Π is a tuple (µ, ME,Mi1,...,Miq), where µ is a membrane structure obtained by removing from µ all membranes different from i1,...,iq Π (of course, the skin membrane cannot be removed), ME is the multiset of objects contained in the environment of µ, andMijis the multiset of objects contained in the region ij. For every multiset m over Σ (the input alphabet of the P system), the initial configuration of Π with input m isthetuple(µ , ∅, M1, ..., MiΠ ∪ m, ..., Mp). Π That is, in any initial configuration of Π the environment is empty. We will denote by IΠ the collection of possible inputs for the system Π. Given a configuration C of a P system Π, applying properly the evolution rules as described above, we obtain, in a non-deterministic way, a new configuration C ′ .WedenotebyC⇒C Π ′ , and we say that we have a transition from C to C ′ .Ahalting configuration is a configuration in which no evolution rule can be applied. A computation C of a P system is a sequence of configurations, {Ci }i
The P Versus NP Problem Through Cellular Computing with Membranes 343 Definition 4. The output of a computation C = {C i }i
Page 1 and 2:
Lecture Notes in Computer Science 2
Page 3 and 4:
Nata˘sa Jonoska Gheorghe Păun Grz
Page 5 and 6:
Thomas J. Head
Page 7 and 8:
VIII Preface portant to keep in min
Page 9 and 10:
X Table of Contents Formal Properti
Page 11 and 12:
Solving Graph Problems by P Systems
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
where Solving Graph Problems by P S
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Writing Information into DNA Masano
Page 35 and 36:
Writing Information into DNA 25 Ham
Page 37 and 38:
Writing Information into DNA 27 Fig
Page 39 and 40:
Writing Information into DNA 29 Dea
Page 41 and 42:
5 Results 5.1 DNA Code for the Engl
Page 43 and 44:
Writing Information into DNA 33 3.
Page 45 and 46:
Writing Information into DNA 35 101
Page 47 and 48:
Balance Machines: Computing = Balan
Page 49 and 50:
+ .. . + Balance Machines: Computin
Page 51 and 52:
x Balance Machines: Computing = Bal
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
1 Balance Machines: Computing = Bal
Page 59 and 60:
Eilenberg P Systems with Symbol-Obj
Page 61 and 62:
2 Definitions Definition 1. A strea
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
5 Conclusions Eilenberg P Systems w
Page 71 and 72:
Molecular Tiling and DNA Self-assem
Page 73 and 74:
3 Molecular Self-assembly Processes
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
8 Hierarchical Tiling Molecular Til
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
References Molecular Tiling and DNA
Page 93 and 94:
Page 95 and 96:
On Some Classes of Splicing Languag
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
ˆxa ˆby ✬ ✩✬ ✩ a b x y
Page 115 and 116:
Page 117 and 118:
The Power of Networks of Watson-Cri
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Fixed Point Approach to Commutation
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Here the last one holds if and only
Page 137 and 138:
Page 139 and 140:
� � � � � Fixed Point App
Page 141 and 142:
Page 143 and 144:
Remarks on Relativisations and DNA
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Splicing Test Tube Systems and Thei
Page 151 and 152:
Splicing Test Tube Systems 141 the
Page 153 and 154:
Splicing Test Tube Systems 143 to a
Page 155 and 156:
Splicing Test Tube Systems 145 6. R
Page 157 and 158:
Splicing Test Tube Systems 147 (c)
Page 159 and 160:
I0 Ai i Splicing Test Tube Systems
Page 161 and 162:
Splicing Test Tube Systems 151 4. J
Page 163 and 164:
Digital Information Encoding on DNA
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
DNA-based Cryptography Ashish Gehan
Page 179 and 180:
DNA-based Cryptography 169 concern.
Page 181 and 182:
DNA-based Cryptography 171 The one-
Page 183 and 184:
DNA-based Cryptography 173 of DNA t
Page 185 and 186:
DNA-based Cryptography 175 Fig. 3.
Page 187 and 188:
DNA-based Cryptography 177 the comp
Page 189 and 190:
DNA-based Cryptography 179 can be c
Page 191 and 192:
DNA-based Cryptography 181 4.4 DNA-
Page 193 and 194:
DNA-based Cryptography 183 Fig. 7.
Page 195 and 196:
DNA-based Cryptography 185 offer li
Page 197 and 198:
DNA-based Cryptography 187 30. C. M
Page 199 and 200:
Splicing to the Limit Elizabeth Goo
Page 201 and 202:
Splicing to the Limit 191 molecular
Page 203 and 204:
Splicing to the Limit 193 Discussio
Page 205 and 206:
Example 9. The splicing rules are S
Page 207 and 208:
−2α � kNNk = −2αMN, k α
Page 209 and 210:
Finally we define the limit languag
Page 211 and 212:
6 Conclusion Splicing to the Limit
Page 213 and 214:
Formal Properties of Gene Assembly
Page 215 and 216:
(a) (b) Formal Properties of Gene A
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
n-Insertion on Languages Masami Ito
Page 225 and 226:
n-Insertion on Languages 215 3. ∀
Page 227 and 228:
n-Insertion on Languages 217 Theore
Page 229 and 230:
Transducers with Programmable Input
Page 231 and 232:
Page 233 and 234:
1 01 s 0 Transducers with Programma
Page 235 and 236:
order β l Transducers with Program
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
start tile Transducers with Program
Page 249 and 250:
Page 251 and 252:
Methods for Constructing Coded DNA
Page 253 and 254:
Page 255 and 256:
u u Methods for Constructing Coded
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
On the Universality of P Systems wi
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
An Algorithm for Testing Structure
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Definition 1. Define the relation
Page 291 and 292:
280 Manfred Kudlek Definition 5. Co
Page 293 and 294:
On Languages of Cyclic Words 283 Th
Page 295 and 296:
On Languages of Cyclic Words 285 No
Page 297 and 298:
On Languages of Cyclic Words 287 Th
Page 299 and 300:
A DNA Algorithm for the Hamiltonian
Page 301 and 302: A DNA Algorithm for the Hamiltonian
Page 307 and 308: Formal Languages Arising from Gene
Page 319 and 320: A Proof of Regularity for Finite Sp
Page 325 and 326: --- ◦ ❄ ⊗ γ ✲ A Proof of R
Page 329 and 330: The Duality of Patterning in Molecu
Page 331 and 332: The Duality of Patterning in Molecu
Page 333 and 334: Membrane Computing: Some Non-standa
Page 335 and 336: where: Membrane Computing: Some Non
Page 337 and 338: where: Membrane Computing: Some Non
Page 349 and 350: The P Versus NP Problem Through Cel
Page 351: The P Versus NP Problem Through Cel
Page 363 and 364: Realizing Switching Functions Using
Page 365 and 366: Realizing Switching Functions Using
Page 367 and 368: AND Gate Realizing Switching Functi
Page 369 and 370: NOR Gate Realizing Switching Functi
Page 371 and 372: Plasmids to Solve #3SAT Rani Siromo
Page 373 and 374: Plasmids to Solve #3SAT 363 A comme
Page 375 and 376: Plasmids to Solve #3SAT 365 from th
Page 377 and 378: Communicating Distributed H Systems
Page 383 and 384: Proof Communicating Distributed H S
Page 395 and 396: Books: Publications by Thomas J. He
Page 397 and 398: Publications by Thomas J. Head 387
Page 399 and 400: Publications by Thomas J. Head 389
show all

LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

Create successful ePaper yourself

Delete template?

Save as template?