a machine modeled within the 1930's to ascertain whether an algorithm could be depicted and utilized to prove any mathematical problem which was provable. The Turing machine had four elements: a finite-state machine, an infinite tape, an alphabet of tokens, and a read/write head which was utilized for reading and documenting data generated by the finite-state machine from and onto the tape. The tape was infinite just in that it was expected which the read/write head would consistently be provided with information in addition to have space to write new information. There are many manners of depicting the state of the Turing machine. One approach is with a group of five values, provided by the alphabet of tokens: (i) the next state of the finite-state machine, (ii) the token written to the tape, (iii), (iv) the instruction for progressing the read/write head, and (v) the state of the finite-state machine, the token read from the tape. Sets of these trends of five tokens combined are what comprise the program for the machine.