The Turing machine is an abstract model of computation invented by mathematician Alan Turing in 1936. It is a mathematical model of a machine that defines computation. JFLAP is educational software written in Java for experimenting with topics in automata theory and formal languages. The Turing machine uses a transition table to change states based on the present state and tape symbol, putting strings starting with 'a' followed by 'b' into an infinite loop and accepting strings starting with 'a' not containing 'b'.