Counter Machine - Problems With The Counter Machine Model

Problems With The Counter Machine Model

The problems are discussed in detail in the article Random access machine. The problems fall into two major classes and a third "inconvenience" class:

(1) Unbounded capacities of registers versus bounded capacities of state-machine instructions: How will the machine create constants larger than the capacity of its finite state machine?

(2) Unbounded numbers of registers versus bounded numbers of state-machine instructions: How will the machine access registers with address-numbers beyond the reach/capability of its finite state machine?

(3) The fully reduced models are cumbersome:

Shepherdson and Sturgis (1963) are unapologetic about their 6-instruction set. They have made their choice based on "ease of programming... rather than economy" (p. 219 footnote 1).

Shepherdson and Sturgis' instructions ( indicates "contents of register r"):

  • INCREMENT ( r ) ; +1 → r
  • DECREMENT ( r ) ; -1 → r
  • CLEAR ( r ) ; 0 → r
  • COPY ( rs to rd ) ; → rd
  • JUMP-UNCONDITIONAL to instruction Iz
  • JUMP IF =0 to instruction Iz

Minsky (1967) expanded his 2-instruction set { INC (z), JZDEC (r, Iz) } to { CLR (r), INC (r), JZDEC (r, Iz), J (Iz) } before his proof that a "Universal Program Machine" can be built with only two registers (p. 255ff).

Read more about this topic:  Counter Machine

Famous quotes containing the words problems, counter, machine and/or model:

    “We are all adult learners. Most of us have learned a good deal more out of school than in it. We have learned from our families, our work, our friends. We have learned from problems resolved and tasks achieved but also from mistakes confronted and illusions unmasked. . . . Some of what we have learned is trivial: some has changed our lives forever.”
    —Laurent A. Daloz (20th century)

    “As deaths have accumulated I have begun to think of life and death as a set of balance scales. When one is young, the scale is heavily tipped toward the living. With the first death, the first consciousness of death, the counter scale begins to fall. Death by death, the scales shift weight until what was unthinkable becomes merely a matter of gravity and the fall into death becomes an easy step.”
    —Alison Hawthorne Deming (b. 1946)

    “The cycle of the machine is now coming to an end. Man has learned much in the hard discipline and the shrewd, unflinching grasp of practical possibilities that the machine has provided in the last three centuries: but we can no more continue to live in the world of the machine than we could live successfully on the barren surface of the moon.”
    —Lewis Mumford (1895–1990)

    “AIDS occupies such a large part in our awareness because of what it has been taken to represent. It seems the very model of all the catastrophes privileged populations feel await them.”
    —Susan Sontag (b. 1933)