Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001 Association of Mizar Users

## Introduction to Turing Machines

Jing-Chao Chen
Bell Labs Research China, Lucent Technologies, Bejing
Yatsuka Nakamura
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.

#### MML Identifier: TURING_1

The terminology and notation used in this paper have been introduced in the following articles [18] [9] [24] [2] [21] [3] [15] [1] [22] [14] [19] [17] [6] [7] [12] [4] [11] [20] [10] [8] [16] [23] [13] [25] [5]

#### Contents (PDF format)

1. Preliminaries
2. Definitions and Terminology for Turing Machine
3. Summation of Two Natural Numbers
4. Computing Successor Function
5. Computing Zero Function
6. Computing \$n\$-ary Project Function
7. Combining Two Turing Machines into One

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