基于粘贴与删除系统求解最短有向路问题的DNA计算模型

{
γ 2 = (V2 , T , A2 , R ) ,
݊Ё
V2 = V1 , R = {wi i , Mv i / λ , wi
}
ˈ
DŽ
᳔‫ڱ‬᳝৥Ჳ ਜ਼ ⊩ ଡ଼᯸Ϣߴ┨ிඣ∖ᢧ᳔‫ڱ‬᳝৥Ჳ⒲Lਜ਼⊩
߽ Ϭ ଡ଼ ᯸ ி ඣ ϣ៤ᔶ བ Ոऩ ⏂ ߚ ᄤ DŽ ߽ Ϭ ߴ ┨ ி ඣ ϣ៤ᔶ བ Ոऩ ⏂ ߚ ᄤ DŽ ᪿߎ ⑃ ᑺ ᳔ ‫ ڱ‬Ոህ ᰃ ᠔ ∖ ᳔ ‫ ڱ‬᳝ ৥ Ჳ DŽ ∖ ᢧ ᳔ ‫ڱ‬ ᳝ ৥ Ჳ ⒲ L Ո ਜ਼ ⊩ Ո ᅲ ɴ ' 1 $ ේ ‫ۅ‬ ᇍ ଡ଼ ᯸ ி ඣ Ё Ո Ϣ Ё ‫ ܗ‬௤ ẟ ᜐ ේ ‫ ۅ‬DŽϬ ⑃ ᑺ Ў Ո ᑣ ߫ ේ ‫ۅ‬ Ϣ ˄ ˅DŽ Ոේ ‫ ⑃ ۅ‬ᑺ প ‫ އ‬Ѣ Ոؐ བ Ϭ ⑃ ᑺ Ў Ո ᑣ ߫ ේ ‫ ۅ‬DŽ ϣ ĭ ᪡ ԰ ℹ ɘ
Abstract
˖
Shortest directed path problem is finding a directed path with minimum weight in two pointed
vertex of a directed network. It has extensive application in engineering practice. Sticker system and delete system are two kinds of basic models in DNA computing form model.This paper proposed DNA computing model and biochemical procedures of graph shortest directed path problem useing high parallelism of sticker system and delete system. Key words: DNA computing sticker system delete system shortest directed path problem
γ
LM n (γ ) = w ∈ WK ρ (V ) x ⇒ ∗ w, x ∈ A x, y ∈ LR ρ (V ) x⇒ ∗ w
x⇒ y
D
(u, v ) ∈ D (u, v )
y = µ (u , µ ( x, v ))
WK ρ (V )
,
α = xuwvyz
,
DNA
,
x, u , w, v, y , z
γ2
Mv1 w1i1 wi1i2 L wi j n Mv n M Mv1 w1i1 wi1i2 L wi j n Mv n M
γ1
Mv1 w1i1 L Mv ik wik ik +1 L Mv n M
γ1
A1
D
l
DNA 5
vi (i = 1,2, L , n) wij
M
l∈Z+
wij
wij
,
wij =5,
(1College of Information Science and Engineering. Shandong University of Science and Technology. Qingdao 266510; 2 College of Information. Shandong University of Science and Technology. taian 271209)
ρ
w1 , w2 ∈ V ∗
w1
w2 ᅗ ᰃଡ଼ ᯸ ி ඣ Ո Џ ᡅ Ẕ ਜ਼ DŽ ߾˖
x = x1 x 2 x3 ∈ Wρ (V ) y ∈ W ρ (V )

DŽ Ոଡ଼ ᯸ Ẕ ਜ਼ བ ϟ೒ ᠔
x, y
ᰃ ᇍ ࢴ݇ ி DŽࢴ Ўଡ଼᯸ிඣ ѻϣ { }ˈ Ո᪱ ᣄ ݊ Ё ᔧϨҙᔧᇍ ˈ ˈ DŽ ᜬ ߾Ң ߎ থ ඓ ẋ Ϟ Ոϔ ᇍ ໮ ଷ ᪾ ɜ ᥦ ԰ Ϭ ϣ ៤ Ё Ոᅠ ᭈ ঠ ⏂ ߚ ᄤ DŽ ߴ ┨ Ẕ ਜ਼ ᰃ ߴ ┨ ி ඣ ՈЏ ᡅ Ẕ ਜ਼ Ở ẋ ⏝ ‑ ϢỄ ☿ ᪡ ԰ ᡔ ᴃ ѻ ϣ ϔ ࢑ ᪱ ᣄDŽ ߴ ┨ Ẕ ਜ਼ ৃ ᢧ ₎ བ ϟ˖᪂ ᰃ ϔ ᴵ ऩ ⏂ ݊ Ё ᄤ ⏂ ῁ ᰃ ऩ ⏂ ˈ Ϣ঺ ໪ ϔ ᴵ ऩ ⏂ ᴖ Ѹ ݊ Ё ˈ ߚ ߿ ᰃ ऩ ⏂ Ոᜩ Ϣ ඗ ড় Ϣ ඗ ড় ᡬ ঴ DŽϬ ‫ ߛ ݙ‬Ḍ ‼ › এ ᥝ ɳ ࡴ ܹ ऩ ⏂ ੠ ༞ ড় › ᕫ ࠄ ᅠ ᭈ ঠ ⏂ ࡴ ⛁ Ở ẋ ব ᗻ Փ ঠ ⏂ ব ៤ ऩ ⏂ DŽϞ Ẵ Ẕ ਜ਼ ߴ ┨ њ Ё Ոऩ ⏂ ᑣ ߫ DŽ ߴ┨ிඣ ݊Ё ᰃ ᄫ ↡ ᜬ Ё‫ ܗ‬௤ Ў ϝ ‫ ܗ‬ඈ ݊ Ё DŽ ᜬ ߾ ೼ Ϟ ϟ ᭛ Ёߴ ┨ ੄ ᩴ Ў }Ў ߴ ┨ ி ඣ ѻ ϣ Ո ᪱ ᣄ ˈ݊Ё DŽ { ᜬ߾Ңߎথˈ ඓ ẋ Ёߴ ┨ ᢈ ߭ ԰ Ϭ ˈϣ ៤ Ёऩ ⏂ ߚ ᄤ DŽ ᪂ ᰃ ϔ Ͼ ᳝ ৥ ต ච ݊Ё ߚ ߿ ᰃ Ո * ⚍ ▊ ṽ ▊ ੠ ᴗ ▊ DŽ᳔ ‫ ڱ‬᳝ ৥ Ჳ ⒲ L ህ ᰃ ೼ ϔ Ͼ ᳝ ৥ ต ච ЁՈ ϸ Ͼ ᣛ ᅮ * ⚍ П Ⓒ ᡒ ߎ ϔ ᴵ ‫ ݋‬᳝ ᳔ ᇣ ᴗ Ո Ჳ DŽᴀ᭛⍝ ঞ Ո ೒ ῁ ᰃ ᴗ ؐ Ў ਍Ҏ ᦤߎњ∖ᢧ᳔‫ڱ‬᳝৥Ჳ⒲LՈϔ࢑ ਜ਼⊩DŽ ℷᭈ᭄ՈϹḐ᳝৥೒DŽ ᑈ
, .
DNA
.
DNA
DNA Computing Model for Shortest Directed Path Problem Based on Sticker and Delete System
Ma Fangfang1, Wang Shudong1, Li Han2, Xue Shengwei1
V1 = V ∪ W ∪ {M } , M
,
M v1 w1i1 ∈ w W ρ (x ) = x , x ∈ V1 , A1 = , 1 i λ 1 M
λ Mv n M λ Mvi k wik ik +1 vi ∈ V , wi i ∈ W , D = , , v M , λ k k k +1 v ik wik ik +1 M λ n
(u, v )
uα v → uv L(γ ) = ω ∈ T ∗ x⇒ ∗ω , x ∈ A
R
γ
x ⇒∗ w
x
T*
G = (V , E , W )
V , E ,W
G
2004
Zuwairie Ibrahim
[7 ]
DNA
2

ᑈ ਍Ҏ ߽Ϭ ᩥਜ਼῵ᢳњ ਜ਼⊩∖ᢧ᳔‫ڱ‬᳝৥Ჳ⒲LDŽ ᭛Ё᳾ ҟ එ Ո ᴃ ᪱ Ϣ ᩴ ো ᢅ খ ໇ ᭛Dz DŽ ிඣՈᵘỤ ᪂ ᰃ ϔ Ͼ ᳝ ৥ ต ච ݊Ё ߚ ߿ ᰃ Ո * ⚍ ▊ ṽ ▊ ੠ ᴗ ▊ ˈ݊Ё ˈ ᰃ ṽ Ϟ Ո ᴗ ؐ DŽϟ ☦ ៥ Ӏ ᵘ Ụ ࿁ ῵ ᢳ Ϟ Ẵ ᳝ ৥ ต ච ЁҢ* ⚍ ࠄ * ⚍ Ո ᳔ ‫ ڱ‬᳝ ৥ Ჳ Ո ϣ ៤ ி ඣ DŽ ଡ଼ଡ଼ ᯸ ி ඣ Ոᵘ Ụ ݊Ё ᰃϔϾ৪ো ᇍ ࢴ ݇ ி ᵘỤଡ଼᯸ிඣ
DNA
3

ᇚ ේ ‫ ۅ‬ད Ո Ёऩ ⏂ ߚ ᄤᬒ ܹ ৿ ᳝ ϡ ᅠ ᭈ ঠ ⏂ ߚ ᄤ Ո᪙ ੥ Ё ࡴ ܹ ෗ ‫ ⎆ ކ‬੠ Ả ᥹ › ϡ ᅠ ᭈ ߚ ᄤ৥ ে ẟ ᜐ ᓊ Ԍ ᪡ ԰ ϣ ៤ ߱ ྟ ᭄ ᥂ ∴ DŽ߽ Ϭ ᥶ ⍌ ߚ ࡿ ߎ ᏺ ᳝ ଡ଼ ᗻ ᳿ ঳ Ոϡ ᅠ ᭈ ঠ ⏂ ߚ Ոऩ ⏂ ߚ ᄤDŽ ᄤࡴ ⛁ ᪙ ੥ ϣ ៤ ᔶ བ ೼ࣙ৿ Ո᪙ ੥ Ёࡴ ܹ ↣ ᴵ ṽ ᴗ Ոᜩ Ϣ‫ ߛ ݙ‬Ḍ ‼ › ǃẢ ᥹ › এ ┨ Ϣ П Ⓒ Ո* ⚍ ᕫ ࠄᔶ བ Ոऩ ⏂ ߚ ᄤDŽ ᇚ ẝ ѯ ऩ ⏂ ߚ ᄤỞẋ ̀ ࿆ ச ⌚ ‫ޱ‬ ྺ Ϲ ⋇ ᡒ ߎ ⑃ ᑺ ᳔ ‫ڱ‬ Ո ߚ ᄤ✊ ৢ ẟ ᜐ ⌟ ᑣ ˈᪿ ߎ * ⚍ . ᑣ ᅲ ẝ՟ ߚϾ *ᵤ ⚍ . ᑣ े Ў ᳔ ‫ ڱ‬᳝ ৥ Ჳ Ჳ ᕘ DŽ ᅲᅲ ՟ Ў њ ᪸ ᯢ ϞẴ ਜ਼ ⊩ Ոৃ ᜐ ᗻ ៥ Ӏ ҹ ೒ Ў ՟ ∖ ᢧ ೒ Ёҹ Ў ྟ ⚍ Ў ඌ ⚍ Ո᳔ ‫ ڱ‬᳝ ৥ Ჳ DŽ
DNA DNA ,
ᕘ ⒲ L ǃ೒ Ո ᳔ ໻ ಶ ⒲ L ǃ᳔ ໻ ư এ ▊ ⒲ L ǃ೒ ؄ ᄶ ⒲ L ਍ DŽ ᪂ ᰃᄫ ↡ ᜬ ᰃ Ϟ Ո ᇍ ࢴ ݇ ி े ᇍ ᄫ ↡ ᜬ ЁՈ ӏ ᛣ ‫ ܗ‬௤ Ёᄬ ೼ ঺ ϔ Ͼ ‫ ܗ‬௤ ⒵ ᱷ Ϩ() DŽ ߚ߿ᜬ߾Ꮊ঳Ўऩ⏂ে঳Ўঠ⏂Ꮊ঳Ўঠ⏂ ে ঳ Ў ऩ ⏂ ϸ ঳ Ў ऩ ⏂ ЁⒸ Ў ঠ ⏂ Ո ϡ ᅠ ᭈ ঠ ⏂ ߚ ᄤ ᵘ ៤ Ո ▊ ড় DŽҸ ˙ DŽ‫ ܗ‬௤ ࢴЎঠ⏂ᑣ߫៪ߚᄤ݊Ё ˈ Ϣ ⑃ ᑺ ּ ਍ Ϩ⒵ᱷ Ϟ Ո ᇍ ࢴ ݇ ி DŽ ଡ଼ ᯸ Ẕ ਜ਼ ᰃ೼ ϡ ᅠ ᭈ ߚ ᄤ ▊ ড় Ё῵ ᢳ ϣ ĭ ᪡ ԰ ЁՈ Ả ᥹ ᪡ ԰ ϢỄ ☿ ᪡ ԰ ᡔ ᴃ ѻ ϣ ᪱ ᣄ
Ln (γ 1 ) = Mv1 w1i1 L Mvik wik ik +1 L Mv n M vik ∈ V , wik ik +1 ∈ W
{
}
DŽ
}
k k +1 k +1 k + 1ik + 2
ߴ ߴ ┨ ி ඣ Ոᵘ Ụ ᵘỤߴ┨ிඣ
DNA step 1 step 2 step 3
A2 = Ln (γ 1 ) , Ln (γ 2 ) = Mv1 w1i1 wi1i2 L wi j n Mv n M w1i1 , wi1i2 , wi j n ∈ W

෎Ѣଡ଼᯸Ϣߴ┨ிඣ∖ᢧ᳔‫ڱ‬᳝৥Ჳ⒲LՈ ᩥ ਜ਼ ῵ ൟ
Ƞᅷᅷ ɏ ⎥ ᷟ ᴢ ⎉ ᑟ ೷ ӳ