@MISC{TURING_1.MIZ,
  AUTHOR = {Chen, Jing-Chao and Nakamura, Yatsuka},
  TITLE = {Introduction to {T}uring Machines},
  SECTION1 = {Preliminaries},
  SECTION2 = {Definitions and Terminology for Turing Machine},
  SECTION3 = {Summation of Two Natural Numbers},
  SECTION4 = {Computing Successor Function},
  SECTION5 = {Computing Zero Function},
  SECTION6 = {Computing $n$-ary Project Function},
  SECTION7 = {Combining Two Turing Machines into One},
  DAY = {27},
  MONTH = {July},
  YEAR = {2001},
  ADDRESS1 = {Bell Labs Research China
Lucent Technologies
Bejing},
  ADDRESS2 = {Shinshu University\\Nagano},
  SUMMARY = {A Turing machine can be viewed as a simple kind of computer,
   whose operations are constrainted to reading and writing symbols
   on a tape, or moving along the tape to the left or right. 
 In theory, one has proven that the computability
   of Turing machines is equivalent to recursive functions. This
   article defines and verifies the Turing machines of summation and three
   primitive functions which are successor, zero and project functions.
   It is difficult to compute sophisticated functions by simple Turing
   machines. Therefore, we define the combination of two Turing machines.}}

