1. Horn Clause Computation with DNA Molecules
Satoshi Kobayashi
Journal of Combinatorial Optimization, v.3 pp , 1999
Summarized by In-hee Lee

2. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
1.Introduction
Horn program
Subclass of the formulas of first-order logic
Have cloas relation to PROLOG language.
Finite set of Horn clauses is computationally equivalent to Turing machine.
Its parallel implementation with huge number of molecules might have possibility to overcome the computational power of conventional computers.
Propose an experimental method for implementing deduction with a subclass of Horn programs.
(C) 2001, SNU Biointelligence Lab, 

3. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
2.Simple Horn Program
Simple Horn clause
Three disjoint sets C, V, R
C: set of constants, V: set of variables, R: set of relation symbols
Each relation symbol A is associated with nonnegative integer, arity, ary(A)
Connectives and a quantifier
Simple atomic formula(atom):
Simple ground atom(ground atom)
Simple Horn clause(clause):
Fact(n=0), rule(n>0)
Head
Body
(C) 2001, SNU Biointelligence Lab, 

4. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
2.Simple Horn Program
Herbrand base of H (BH)
The set of all ground atoms with relation symbols and constants used in H.
Substitution
A mapping from V to VC.
A ground instance is an expression which doesn’t contain any variable.
Immediate consequence operator TH(I)
The set of all ground atoms can be proved by one step derivation using I and H.
(C) 2001, SNU Biointelligence Lab, 

5. 3.Deduction with DNA Molecules
Elementary form of simple Horn program
Corresponding to graph G(H)=(V,E)
The arguments of every rule are only variables
Any relation symbol appear in the body of rule at most once.
Any variable appears in the body of rule at most two.
Every fact is ground
Every variable appeared in the head of a rule must appear in the body of that rule
Corresponding graph is bipartite.
(C) 2001, SNU Biointelligence Lab, 

6. 3.Deduction with DNA Molecules
(C) 2001, SNU Biointelligence Lab, 

7. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
3.1 Overall Procedure
(C) 2001, SNU Biointelligence Lab, 

8. 3.2 Representation of Atoms
(C) 2001, SNU Biointelligence Lab, 

9. 3.2 Representation of Atoms
Since G(H) is bipartite, V can be divided two disjoint set V1 and V2.
V1:
V2:
(C) 2001, SNU Biointelligence Lab, 

10. 3.3 Argument Equality Check
For every pair (Ai, Bj) in G(H)
Add by ligation and run whiplash PCR with {A, C, T}
Destroy the binding to beads
Extract strands which have by beads.
Amplify extracted strands
(C) 2001, SNU Biointelligence Lab, 

11. 3.3 Argument Equality Check
(C) 2001, SNU Biointelligence Lab, 

12. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
3.4 Argument Copy
For every variable x in head of a rule r and edge(x, y) in G(H)
Argument copy(x, y)
(C) 2001, SNU Biointelligence Lab, 

13. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
3.4 Argument Copy
Copying ith argument of A to jth argument of B
(C) 2001, SNU Biointelligence Lab, 

14. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
3.4 Argument Copy
Example: make A(d1, d3) from B(d1, d2)C(d3, d4) C2 D4 C1 D3 B2 D2 B1 D1 A1 D1 B1 A2 D3 C1 C1 D3 A2 C2 D4 C1 S3 B2 D2 B1 D1 D3 A2 A1 A2 D3 A2 A1 D1 A1 A2 D3
(C) 2001, SNU Biointelligence Lab, 

15. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
4. Discussion
The feasibility of the proposed methods depends on that of whiplash PCR.
Too much human intervention.
(C) 2001, SNU Biointelligence Lab,