LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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208 Tero Harju, Ion Petre, and Grzegorz Rozenberg 5 The Overlap Equivalence Problem The mapping w ↦→ γw of legal strings to overlap graphs is not injective. Indeed, for each legal string w = w1w2, wehave γw1w2 = γw2w1 and γw = γ c(w) , where c is any morphism that selects one element c(p) fromp = {p, p} for each p (and then obviously c(p) =c(p)). In particular, all conjugates of a legal string w have the same overlap graph. Also, the reversal w R and the complementation w C of a legal string w define the same overlap graph as w does. Example 10. The following eight legal strings of pointers (in ∆ � )havethesame overlap graph: 2323, 3232, 2323, 3232, 2323, 3232, 2323, 3232. ✷ Example 11. All string representations of an overlap graph γ need not be obtained from a fixed representation string w by using the operations of conjugation, inversion and reversing (and by considering isomorphic strings equal). For instance, the strings v1 = 23342554 and v2 = 35242453 define the same overlap graph (see Fig. 3), while v1 is not isomorphic to any signed string obtained from v2 by the above operations. However, we will demonstrate that if strings u and v are realistic, then γu = γv implies that u and v can be obtained from each other by using the operations of conjugation, inversion and reversing. ✷ ✎☞ ✍✌ 4 − ✎☞ ✍✌ 2 − ✎☞ ✍✌ 5 − ✎☞ ✍✌ 3 − Fig. 3. The common overlap graph of legal strings v1 = 23342554 and v2 = 35242453. The signed string v1 and v2 are not obtainable from each other by the operations of conjugation, reversal and complementation Examples 10 and 11 lead naturally to the overlap equivalence problem for realistic legal strings: whendotworealistic legal strings u and v have the same overlap graph, i.e., when γu = γv? To solve this problem, we begin by characterizing legal substrings of realistic legal strings. For a signed string v ∈ ∆ � ,let vmin =min(dom(v)) and vmax = max(dom(v)) . Thus, dom(v) ⊆ [vmin,vmax].
Formal Properties of Gene Assembly 209 Example 12. The string v = 48348 3 is legal. We have dom(v) ={3, 4, 8}, and hence vmin =3andvmax =8. ✷ Lemma 1. Let u be a realistic legal string with dom(u) =[2,κ], andletv be a legal substring of u. Then either dom(v) =[p, q] or dom(v) =[2,κ] \ [p, q], for some p and q with p ≤ q. Proof. Let u = u1vu2 - without loss of generality we can assume that u1 and u2 are not both empty strings. (a) Assume that there exists a pointer p with vmin
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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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Digital Information Encoding on DNA
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Page 177 and 178: DNA-based Cryptography Ashish Gehan
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Page 185 and 186: DNA-based Cryptography 175 Fig. 3.
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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
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Page 211 and 212: 6 Conclusion Splicing to the Limit
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On the Universality of P Systems wi
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An Algorithm for Testing Structure
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Definition 1. Define the relation
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280 Manfred Kudlek Definition 5. Co
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On Languages of Cyclic Words 283 Th
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On Languages of Cyclic Words 285 No
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On Languages of Cyclic Words 287 Th
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A DNA Algorithm for the Hamiltonian
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Formal Languages Arising from Gene
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A Proof of Regularity for Finite Sp
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--- ◦ ❄ ⊗ γ ✲ A Proof of R
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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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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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