Theoretical and Experimental DNA Computation (Natural ...

44 2 Theoretical Computer Science: A Primer
and showed how they may be pieced together to perform computations. We
then considered the nature of computation itself, and introduced the concept
of an algorithm. This motivated the study of machine models, or models of
computation. We introduced several such models (the finite-state automaton,
the Turing machine, andtheRandom Access Machine), and described their
features, strengths, and weaknesses. We then considered the implementation
of algorithms within these models, introducing the organization of information
into data structures. We examined a simple data structure, the array, before
considering a more complex structure, the graph. We then highlighted the
fact that different algorithms require different resources, introducing the key
concept of computational complexity. We described the importance of this
idea, and showed how to calculate the complexity of algorithms. This then
motivated a discussion of how to choose an algorithm for a particular problem.
We concluded with a description of complexity classes, and introduced the
NP-complete problems, for which no fast algorithms yet exist.
2.9 Bibliographical Notes
A standard textbook on computer architecture is [149], which includes a treatment
of Boolean algebra. Algorithms and complexity are introduced in [48]
(which also covers sorting networks, encountered in Chap. 5). Another classic
text on data structures and algorithms is [5]. For an excellent introduction to
the theory of graphs, see [67]. The controversial 2 paper that first established
that any planar graph is four colorable is published as both a book [16] and a
paper [15]. Finally, a discussion of why some problems are inherently difficult
and a treatment of state-of-the art solution methods are given in [107].
2 Due to its reliance on computer-assisted proof.