Monday, September 17, 2001
Formal Definition of Turing Machines
In this lecture we went in painstaking detail through the definition of a Turing machine in Sipser to reinforce our skills for reading and understanding mathematical definitions. We looked at
 | the definition of a Turing machine |
| the discussion of what a Turing machine execution constitutes |
| the fact that everything about a Turing machine is finite, in keeping with the fact that we are trying to understand what is and is not computable; nothing that involves infinite resources can be considered to be computable. |
| what constitutes a configuration of a Turing machine. |
| the fact that Turing machines only accept or reject an input string and are as such nothing but language recognizers |
We also pointed out that every textbook author defines Turing machines differently. This is only because each author has a plan for presenting the theory related to Turing machines in a fashion that is best done in the context of their definition. All of the different ways can be shown through lemmas to be equivalent.