# Designing a turing Machine belonging to a language

Im trying to learn the concept of turing machines.I have understood the basic stuff like its a simple mathematical model of a computer and its parts.Now im asked to create a turing machine.

Design a turing machine that accept strings belonging to the language
(a + b)* from the alphabet (a, b)


Can someone describe to me how it is done?

• What does the "+" denote here? – mrp Dec 7 '14 at 11:35
• @mrp Its a Terminal – techno Dec 7 '14 at 11:41
• So you want to make a Turing machine that accepts everything? – Henning Makholm Dec 7 '14 at 12:16
• The plus is NOT a terminal, $(a+b)^*$ is a regular expression meaning that you choose $a$ or $b$ and then take the Kleene star to iterate this. Hence the expression stands for all strings over the alphabet $\{a,b\}$. – MHS Dec 8 '14 at 13:08
• Now to construct the Turing machine, what do you know about Turing machines? How would you start constructing one piece by piece (selecting the tape alphabet, machine states, transition function/relation etc.)? – MHS Dec 8 '14 at 13:09