Theoretical and Experimental DNA Computation (Natural ...

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f
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a b
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f
3.6 Summary 69
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b
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8
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Initial configuration First iteration, n=1 Second iteration, n=2 Third iteration, n=3
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16
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Fourth iteration, n=4,
dissolve membrane 3
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4 12
d e
f
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3
Replace b with d in Produce copies of e
parallel, halve copies of f
1
4 16
d e
Increase e, halve f f dissolves membrane 2 Send out copies of e,
1
d 4
Increase e, halve f
e 16
Fig. 3.10. Execution of P system for n =4
In terms of their application, P systems have been used to solve instances
of NP-complete problems, notably the Satisfiability and Hamiltonian Path
Problems [165]. It is clear that the emerging field of P systems will provide a
rich vein of both theoretical results and applications. As Gheorge Păun notes
in [117], perhaps the most fundamental open question in the field concerns
the physical realization of P systems. Perhaps research in the field of cellular
computing (discussed in a later chapter) may provide further insights into
this.
3.6 Summary
In this chapter we categorized models of molecular computation into one of
four types (filtering, splicing, constructive, and membrane). Abstract models
of each type were described, as well as a selection of algorithms within them.