demonstrates that only one conditional jump is required, i.e. either J0xxx or J1xxx. However, with this restriction, the machine becomes difficult to write instructions for. Often only two are used, i.e. but the use of all three { J0xxx, J1xxx, Jxxx } does eliminate extra instructions. In the 2-state Busy Beaver example that we use only { J1xxx, Jxxx }. 2-state busy beaver The mission of the busy beaver is to print as many ones as possible before halting. The "Print" instruction writes a 1, the "Erase" instruction (not used in this example) writes a 0 (i.e. it is the same as P0). The tape moves "Left" or "Right" (i.e. the "head" is stationary). State table for a 2-state Turing-machine busy beaver: Instructions for the Post–Turing version of a 2-state busy beaver: observe that all the instructions are on the same line and in sequence. This is a significant departure from the "Turing" version and is in the same format as what is called a "computer program": Alternately, we might write the table as a string. The use of "parameter separators" ":" and instruction-separators "," are entirely our choice and do not appear in the model. There are no conventions (but see Booth (1967) p. 374, and Boolos and Jeffrey (1974, 1999) p. 23), for some useful ideas of how to combine state diagram conventions with the instructions – i.e. to use arrows to indicate the destination of the jumps). In the example immediately below, the instructions are sequential starting from "1", and the parameters/"operands" are considered part of their instructions/"opcodes": J1:5, P, R, J:8, P, L, J:8, J1:12, P, L, J1:1, P, N, J:15, H Notes References Stephen C. Kleene, Introduction to Meta-Mathematics, North-Holland Publishing Company, New York, 10th edition 1991, first published 1952. Chapter XIII is an excellent description of Turing machines; Kleene uses a Post-like model in his description and admits the Turing model could be further atomized, see footnote 1. Martin Davis, editor: The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, Raven Press, New York, 1965. Papers include those by Gödel, Church, Rosser, Kleene, and Post. Martin Davis, "What is a computation", in Mathematics Today, Lynn Arthur Steen, Vintage Books (Random House), 1980. A wonderful little paper, perhaps the best ever written about Turing Machines. Davis reduces the Turing Machine to a far-simpler model based on Post's model of a computation. Includes