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 with, problems, counter, machine and/or model:

    “I conceive that the leading characteristic of the nineteenth century has been the rapid growth of the scientific spirit, the consequent application of scientific methods of investigation to all the problems with which the human mind is occupied, and the correlative rejection of traditional beliefs which have proved their incompetence to bear such investigation.”
    —Thomas Henry Huxley (1825–95)

    “Sustained unemployment not only denies parents the opportunity to meet the food, clothing, and shelter needs of their children but also denies them the sense of adequacy, belonging, and worth which being able to do so provides. This increases the likelihood of family problems and decreases the chances of many children to be adequately prepared for school.”
    —James P. Comer (20th century)

    “Often, when there is a conflict between parent and child, at its very hub is an expectation that the child should be acting differently. Sometimes these expectations run counter what is known about children’s growth. They stem from remembering oneself, but usually at a slightly older age.”
    —Ellen Galinsky (20th century)

    “A multitude of little superfluous precautions engender here a population of deputies and sub-officials, each of whom acquits himself with an air of importance and a rigorous precision, which seemed to say, though everything is done with much silence, “Make way, I am one of the members of the grand machine of state.””
    —Marquis De Custine (1790–1857)

    “...that absolutely everything beloved and cherished of the bourgeoisie, the conservative, the cowardly, and the impotent—the State, family life, secular art and science—was consciously or unconsciously hostile to the religious idea, to the Church, whose innate tendency and permanent aim was the dissolution of all existing worldly orders, and the reconstitution of society after the model of the ideal, the communistic City of God.”
    —Thomas Mann (1875–1955)