By Tom Carter
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To run the machine, it is first set up with a finite input string (from A∗) written on the tape (and the rest of the tape initialized to the blank symbol ’b’). The machine is started in the start state (s0) with its read/write head pointing at the first symbol in the input string. The machine then follows the instructions of the δ function – depending on its current state and the symbol being read in the current tape cell, the machine changes state, writes a (possibly) new symbol in 50 the current tape cell, and then moves the read/write head one cell either left or right.
For example, the regular languages are very concise, easy to work with, and many relevant tools and techniques have been developed. In particular, there has been much research on Markov models. It thus often makes sense to try to develop a regular or Markov approach to your problem, such as the work by Jim Crutchfield on -machines . . Another important example (as indicated above) is work that has been done appliying hidden Markov models to the analysis of genome sequence problems . . 47 Turing machines ← • During the 1930s, the mathematician Alan Turing worked on the general problem of characterizing computable mathematical functions.
One of his deepest insights was that it is possible to encode a Turing machine as a finite string of symbols. Consider a machine T = (S, A, δ, s0, b, F ). Each of S, A, and F is a finite set, and thus can be encoded as a single number (the number of elements in the set). We can assume that s0 is the first of the states, so we don’t need to encode that. We can assume (possibly by reordering) that the states F are at the end of the list of states, so we only need to know how many there are. The symbols in A are arbitrary, so we only need to know how many there are.
Introduction to Theory of Computation by Tom Carter