Queue Automaton - Theory

Theory

We define a queue machine by the six-tuple

where
  • is a finite set of states;
  • is the finite set of the input alphabet;
  • is the finite queue alphabet;
  • is the initial queue symbol;
  • is the start state;
  • is the transition function.

We define the current status of the machine by a configuration, an ordered pair of its state and queue contents (note defines the Kleene closure or set of all supersets of ). Therefore the starting configuration on an input string is defined as, and we can define our transition as the function that, given an initial state and queue, takes the function to a new state and queue. Note the "first-in-first-out" property of the queue in the relation

where defines the next configuration relation, or simply the transition function from one configuration to the next.

The machine accepts a string if after a (possibly infinite) number of transitions the starting configuration evolves to exhaust the string (reaching a null string ), or

Read more about this topic:  Queue Automaton

Famous quotes containing the word theory:

    We have our little theory on all human and divine things. Poetry, the workings of genius itself, which, in all times, with one or another meaning, has been called Inspiration, and held to be mysterious and inscrutable, is no longer without its scientific exposition. The building of the lofty rhyme is like any other masonry or bricklaying: we have theories of its rise, height, decline and fall—which latter, it would seem, is now near, among all people.
    Thomas Carlyle (1795–1881)

    Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.
    Willard Van Orman Quine (b. 1908)

    The things that will destroy America are prosperity-at-any- price, peace-at-any-price, safety-first instead of duty-first, the love of soft living, and the get-rich-quick theory of life.
    Theodore Roosevelt (1858–1919)