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:

    “Our young people are diseased with the theological problems of original sin, origin of evil, predestination, and the like. These never presented a practical difficulty to any man,—never darkened across any man’s road, who did not go out of his way to seek them. These are the soul’s mumps, and measles, and whooping- coughs, and those who have not caught them cannot describe their health or prescribe a cure. A simple mind will not know these enemies.”
    —Ralph Waldo Emerson (1803–1882)

    “I’d take the bus downtown with my mother, and the big thing was to sit at the counter and get an orange drink and a tuna sandwich on toast. I thought I was living large!... When I was at the Ritz with the publisher a few months ago, I did think, “Oh my God, I’m in the Ritz tearoom.” ... The person who was so happy to sit at the Woolworths counter is now sitting at the Ritz, listening to the harp, and wondering what tea to order.... [ellipsis in source] Am I awake?”
    —Connie Porter (b. 1959)

    “Psychiatric enlightenment has begun to debunk the superstition that to manage a machine you must become a machine, and that to raise masters of the machine you must mechanize the impulses of childhood.”
    —Erik H. Erikson (1904–1994)

    “The Battle of Waterloo is a work of art with tension and drama with its unceasing change from hope to fear and back again, change which suddenly dissolves into a moment of extreme catastrophe, a model tragedy because the fate of Europe was determined within this individual fate.”
    —Stefan Zweig (18811942)