LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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Balance Machines: Computing = Balancing 47
2 3
Fig. 16. Balance machine as a “transmission line”. Balance machine (2) acts as a
transmission line feeding the output of machine (1) into the input of machine (3).
+
1
A B 10 5 Extra1A B 10 5 Extra2
′
A
+
A ′
3
Satisfiability of (a + b)(a ′ + b)
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15
2
+ +
a b
Truth table
0 0 0
0 1 1
1 0 0
1 1 1
(a + b)(a ′ + b)
Fig. 17. Solving an instance of SAT: The satisfiability of the formula (a + b)(a ′ + b)
is verified. Machines (1), (2) and (3) work together sharing the variables A, B and A ′
between them. OR gates (labeled 1 and 2) realize (a + b) and(a ′ + b) respectively and
the NOT gate (labeled 3) ensures that a and a ′ are “complementary”. Note that the
“output” of gates (1) and (2) are set to 10. Now, one has to observe the values eventually
assumed by the variable weights A and B (that represent “inputs” of OR gate (1)).
Given the assumptions already mentioned, one can easily verify that the machine will
balance, assuming one of the two following settings: (i) A =5,B = 10, (Extra1 =0,
Extra2 = 5) or (ii) A = 10, B = 10, (Extra1 =5,Extra2 = 0). These are the only
configurations that make the machine balanced. In situations when both the left pans
of gate (1) assume 10, Extra1 will automatically assume 5 to balance off the extra
weight on the left side. (Extra2 plays a similar role in gate (2).)